{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Wmr2Fx9oHsNn"
   },
   "source": [
    "# Tutorial with 1d advection equation\n",
    "\n",
    "Jiawei Zhuang\n",
    "7/24/2019"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-30T03:31:49.716343Z",
     "start_time": "2019-07-30T03:31:47.420771Z"
    },
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 6309,
     "status": "ok",
     "timestamp": 1564033372026,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "QcLNBO0xC0oE",
    "outputId": "65f867ef-460c-4ca6-a575-f7ac3b8dbb86"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1.13.1', '2.2.4-tf')"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.size'] = 14\n",
    "\n",
    "tf.enable_eager_execution()\n",
    "\n",
    "tf.__version__, tf.keras.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-30T03:31:53.771287Z",
     "start_time": "2019-07-30T03:31:52.078721Z"
    },
    "colab": {},
    "colab_type": "code",
    "id": "KXAc1j0UEa24"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.\n",
      "For more information, please see:\n",
      "  * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md\n",
      "  * https://github.com/tensorflow/addons\n",
      "If you depend on functionality not listed there, please file an issue.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import xarray\n",
    "from datadrivenpdes.core import grids\n",
    "from datadrivenpdes.core import integrate\n",
    "from datadrivenpdes.core import models\n",
    "from datadrivenpdes.core import tensor_ops\n",
    "from datadrivenpdes.advection import equations as advection_equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rfMXV3q2F1bP"
   },
   "source": [
    "# Define simulation grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-30T03:32:09.208744Z",
     "start_time": "2019-07-30T03:32:09.204082Z"
    },
    "colab": {},
    "colab_type": "code",
    "id": "8XEBxMtIF4FO"
   },
   "outputs": [],
   "source": [
    "# we mostly run simulation on coarse grid\n",
    "# the fine grid is only for obtaining training data and generate the reference \"truth\"\n",
    "\n",
    "grid_length = 256\n",
    "fine_grid_resolution = 256\n",
    "coarse_grid_resolution = 32\n",
    "\n",
    "assert fine_grid_resolution % coarse_grid_resolution == 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-30T03:32:18.933109Z",
     "start_time": "2019-07-30T03:32:18.923186Z"
    },
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 323,
     "status": "ok",
     "timestamp": 1564033386056,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "xGRaDph3GXKv",
    "outputId": "eb080f5c-b245-4378-8388-91abc76af7ef"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((256, 1), (32, 1))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1d domain, so only 1 point along y dimension\n",
    "\n",
    "fine_grid = grids.Grid(\n",
    "    size_x=fine_grid_resolution, size_y=1, \n",
    "    step=grid_length/fine_grid_resolution\n",
    "    )\n",
    "\n",
    "coarse_grid = grids.Grid(\n",
    "    size_x=coarse_grid_resolution, size_y=1, \n",
    "    step=grid_length/coarse_grid_resolution\n",
    "    )\n",
    "\n",
    "x_fine, _ = fine_grid.get_mesh()\n",
    "x_coarse, _ = coarse_grid.get_mesh()\n",
    "\n",
    "x_fine.shape, x_coarse.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZkRM_J-8ErQ2"
   },
   "source": [
    "# Generate initial condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Djsho1XCEbzW"
   },
   "outputs": [],
   "source": [
    "def make_square(x, height=1.0, center=0.25, width=0.1):\n",
    "  \"\"\"\n",
    "  Args:\n",
    "    x: Numpy array. Shape should be (nx, 1) or (nx,)\n",
    "    height: float, peak concentration\n",
    "    center: float, relative center position in 0~1\n",
    "    width: float, relative width in 0~0.5\n",
    "\n",
    "  Returns:\n",
    "    Numpy array, same shape as `x`\n",
    "  \"\"\"\n",
    "  nx = x.shape[0]\n",
    "  c = np.zeros_like(x)\n",
    "  c[int((center-width)*nx):int((center+width)*nx)] = height\n",
    "  return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 218
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 658,
     "status": "ok",
     "timestamp": 1564033387448,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "OUE3kRDLHLxA",
    "outputId": "5d76bc27-5235-4dda-cf2a-539ab4e4d494"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Rdtw6diY7UShaV7xV3jF2O7viKU4M9gR5Je6KZ4udKLThkbEWe4a8LXZOnqN4MdgTpLaK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\nYII=\n",
      "text/plain": [
       "<Figure size 800x300 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=[8, 3])\n",
    "axes[0].plot(x_fine, make_square(x_fine), marker='.')\n",
    "axes[1].plot(x_coarse, make_square(x_coarse), marker='.')\n",
    "\n",
    "for ax in axes:\n",
    "  ax.set_ylim(-0.1, 1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 498,
     "status": "ok",
     "timestamp": 1564033388116,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "vX5H5yhCId9e",
    "outputId": "f5ae2213-7d56-493f-a996-2e0fa12ad107"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 32, 1)"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_multi_square(x, height_list, width_list):\n",
    "  c_list = []\n",
    "  for height in height_list:\n",
    "    for width in width_list:\n",
    "      c_temp = make_square(x, height=height, width=width)\n",
    "      c_list.append(c_temp)\n",
    "\n",
    "  return np.array(c_list)\n",
    "\n",
    "height_list = np.arange(0.1, 1.1, 0.1)\n",
    "width_list = np.arange(1/16, 1/4, 1/16)  # width is chosen so that coarse-graining of square wave is symmetric\n",
    "\n",
    "c_init = make_multi_square(\n",
    "  x_coarse,\n",
    "  height_list = height_list,\n",
    "  width_list = width_list\n",
    ")\n",
    "\n",
    "c_init.shape  # (sample, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 218
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1042,
     "status": "ok",
     "timestamp": 1564033389302,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "_ryUCombJNU8",
    "outputId": "9e47e05f-7c99-4f57-da44-f04b62037641"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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o5MmT/b4putDWrVu1YsUKPfXUU7rxxhuHbBsIBFRTUzPot0LAaBks49FoNGcz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\nj0Nf2hTg5icAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1600x300 with 5 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 5, figsize=[16, 3])\n",
    "\n",
    "for i, ax in enumerate(axes):\n",
    "  ax.plot(x_coarse, c_init[4*i+2, :, 0], marker='.')\n",
    "  ax.set_ylim(-0.1, 1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YXRdsl-vJxdf"
   },
   "source": [
    "# Wrap with velocity fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 71
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 342,
     "status": "ok",
     "timestamp": 1564033389766,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "SPWm9dvdJ1Ao",
    "outputId": "af222607-d7ee-46d2-8c9b-cabd0aec5691"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "concentration (30, 32, 1)\n",
      "x_velocity (30, 32, 1)\n",
      "y_velocity (30, 32, 1)\n"
     ]
    }
   ],
   "source": [
    "# for simplicity, use uniform constant velocity field for all samples\n",
    "\n",
    "initial_state = {\n",
    "    'concentration': c_init.astype(np.float32),  # tensorflow code expects float32\n",
    "    'x_velocity': np.ones(c_init.shape, np.float32) * 1.0,\n",
    "    'y_velocity': np.zeros(c_init.shape, np.float32)\n",
    "}\n",
    "\n",
    "for k, v in initial_state.items():\n",
    "  print(k, v.shape)   # (sample, x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "i70xlBDTEvis"
   },
   "source": [
    "# Run baseline advection solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jwwq-OovExt1"
   },
   "outputs": [],
   "source": [
    "# first-order finite difference model, very diffusive\n",
    "model_1st = models.FiniteDifferenceModel(\n",
    "    advection_equations.UpwindAdvection(cfl_safety_factor=0.5), \n",
    "    coarse_grid\n",
    "    )\n",
    "\n",
    "# second-order scheme with monotonic flux limiter\n",
    "model_2nd = models.FiniteDifferenceModel(\n",
    "    advection_equations.VanLeerAdvection(cfl_safety_factor=0.5), \n",
    "    coarse_grid\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "I_1vfbfBbYaw"
   },
   "outputs": [],
   "source": [
    "time_steps = np.arange(0, 128+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 89
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2043,
     "status": "ok",
     "timestamp": 1564033392915,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "rU2NtMTAbUnE",
    "outputId": "d03144de-daf4-425d-b23e-747a64163eb9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 322 ms, sys: 12.2 ms, total: 334 ms\n",
      "Wall time: 345 ms\n",
      "CPU times: user 1.33 s, sys: 25.6 ms, total: 1.35 s\n",
      "Wall time: 1.37 s\n"
     ]
    }
   ],
   "source": [
    "%time integrated_1st = integrate.integrate_steps(model_1st, initial_state, time_steps)\n",
    "%time integrated_2nd = integrate.integrate_steps(model_2nd, initial_state, time_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 71
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 398,
     "status": "ok",
     "timestamp": 1564033393413,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "N4VjWPwBcJsJ",
    "outputId": "95590794-d800-4230-ddd3-1b22f4939233"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "concentration (129, 30, 32, 1)\n",
      "x_velocity (129, 30, 32, 1)\n",
      "y_velocity (129, 30, 32, 1)\n"
     ]
    }
   ],
   "source": [
    "for k, v in integrated_1st.items():\n",
    "  print(k, v.shape)   # (time, sample, x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "osE-KfdIqN2E"
   },
   "outputs": [],
   "source": [
    "def wrap_as_xarray(integrated):\n",
    "  dr = xarray.DataArray(\n",
    "      integrated['concentration'].numpy().squeeze(),\n",
    "      dims = ('time', 'sample', 'x'),\n",
    "      coords = {'time': time_steps, 'x': x_coarse.squeeze()}\n",
    "  )\n",
    "  return dr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 236
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 983,
     "status": "ok",
     "timestamp": 1564033394883,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "ROEc3w_JcQ_o",
    "outputId": "a9598ccb-0b86-4a49-e95d-c87495da1737"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.plot.facetgrid.FacetGrid at 0x7f201d90aa90>"
      ]
     },
     "execution_count": 15,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w/gwEQLvxkJ0Oh741XptCPGYkgBBCCCFEngyNlSZRn9oCtxKUG/x7XO9Vi0rXGCEHQq9q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\n57327xU66/CgvADC1DMQty7Bud+VG+w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9K3P6zWFOvznkluXy5bkvScxK5O1jb/PWsbeI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\ne5Obm0vXrl3R62Us1M0opaioqODixYsEBjbdEdCiBOKTTz5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hYWHK2dlZDRkyRO3bt8/W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\n",
      "text/plain": [
       "<Figure size 1107.12x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dr_1st = wrap_as_xarray(integrated_1st)\n",
    "dr_1st.isel(time=[0, 10, 128], sample=[4, 10, 16]).plot(col='sample', hue='time')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 236
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1002,
     "status": "ok",
     "timestamp": 1564033395923,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "6OT78CAxdFxQ",
    "outputId": "2a1affa3-d87b-48f8-8eee-77fa9810bf3d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.plot.facetgrid.FacetGrid at 0x7f201b2f15c0>"
      ]
     },
     "execution_count": 16,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hPFVSqT6Qh3sYQFRYK/jppp+yK38XdkV9gEgITmBs7FiGRwynh6lHk/c4FAdZ\nZVlkFmXy0dGPeP/Q+wBEBUbx1LinmNqnQRnF0fXgZ4HBs5pcJzzQxPGCisv9iJ7xC4Bht8O/fwYl\nJyE8yTfjCFGnsq6HoMR2mmp7NSnRKdoN7uEeEA3FBcURa4llb+FeLKZ+nRBAyF4QovvyuIl6yZIl\nLFmypNnXNm3a1Op7ly9f3mhDDCGEaElplQ2dDnqY2y5hUhSFX2//NTvzd3LfsPsYHTWa4RHD6Wnu\n6fF4NoeNY6XH2Fe0j0+Of8JTW5/iH2H/IKFHAjidcPRL6D9FfaC/RGigyZ0x8YlBM9QA4uiXcN1D\nvhtHCOpLmHIqDwMwIlLDRn53AOF5BgJgeMRwMosySfCfx7myah9MrBUhveDsTm3HFKKLkMXIhRBd\nSmmllVCzHwZ9243Dn538jPWn1rN45GKWpSxjcsLkywoeAPwMfgyLGMa9Q+5l1ZRVGPVGHt/8uNoj\nkbcXyvNg0C3Nvjfc4kel1UGt3Uerv4QnQtRQNYAQwsdcJUwnyw8TYY4g1qLh8qSuAKJH3GW9bUTk\nCHIrc/EzlXdOBqK6FGp9lIUUoguTAEII0aWUVlkJ86B8KftCNiu2ryAlOoVFwxd5ZezYoFienfAs\nB84fYNWeVWr5kk4PA29u9nxXn0ZZlYcN2e0xaCac3gZVJb4bQwjqMxBHyw4wPGJ4s0u1+8yFM2CJ\nVJdCvgyuLEmtIbtzeiCgrn9DiO5FAgghRJdSWmUlNLD18iWrw8rjmx/HZDDx/A3PY9B7b8PKm/rc\nxN0D7+btg2+z7fg66H0dBIY3e64r0HH1bfjEoJmgOOB4WtvnCtEBlbV2MFRypjxH2/IlUAOIy+h/\ncBkSPgSjzkglJ90ZFM245lsmfRCi+5EAQgjRpZRW2gi3tJ6BeHX3qxwuOcyvJvyKGEuM1+fw2NjH\n6B/cm6eMFRT3m9zieWF1S816bSnX5sSNgqAYOPqF78YQAqiodWAJzgVgRITWAcTZy+5/AAgwBjAo\nfBClzhPU2p3YHd5Zd98jrhWjpJFadEMSQAghuhQ1A9FyALHl7BbeO/Qe3x30Xab0nuKTOQQYA3ih\n53VU6HU8XXEAp9L8Q4krA1Fa6cMSJr0eBk2HE1+pe1II4SOVtXZMljPodXqGRQzTbmBFaXcAAWoj\ndbE1C3C6V5LSRFAM6AyylKvoliSAEEJ0KaVV1hYzEEVVRTz97dMMCBvAI2Me8ek8BmTv4HGrP98W\n7XEv83op1zx9moEAtYnbWgGntvh2HNGtVVjt6ALO0C+0HxY/i3YDV5eCrapdJUyg9kHYlGr0/oXa\nbiZnMKpN3xJAiG5IAgghRJdUVL88AAAgAElEQVRRbXVQY3M22wOhKAo/3/pzqmxVvDjpRQKMTZdV\n9d5ESiH7W+5Kms3U3lN5ZfcrHDx/sMlprnn6dClXgMRJ6l4UR9f7dhzRrVXUWnH4ZXdC+VJdCVAH\nAggAgzmnk/aCkABCdD8SQAghugzXN/nNbSK3t2gv/837L0tHL6VfaD/fTuR4GigOdINn8eyEZwny\nC+LP+//c5DR/owGLyUCJL0uYQN2Dov8UdTnXS3YsFcJbSq25OHXVjIwcqe3A7dhErqHewb0JNAaj\nN+d0TiO19ECIbkgCCCFEl+EKIJrrgfj0+KeYjWbuGHCH7ydydD1YoiA+hRD/EGb3m83XZ76mpKbp\nUqo+30zOZdAtUJ6r7k0hhA+UObIAtadAU+3cRM5Fp9PRv8cwDAFnOicDcTEXnBr2XohuafXq1SQm\nJhIQEEBKSgpbtnRuSasEEEKILsPVjHxpD0SVrYp/Zf+L6X2nE+gX6NtJ2Gvh+Ea1cVmv/hV5e//b\nsTvtfHGy6UpI4RYTJVoEEANS1T0pjkgZk/CNSl0WBswkhSZpO3BZDhgDwBLR7ksMCh2G3r+Q81UX\nvDgxD4QkgNMGFQXajiu6lQ8//JClS5fy1FNPsWfPHiZMmMCMGTPIycnptDlJACGE6DJcGYiwS3og\nNpzeQLW9mtsH3O77SWRvBWt5o92nB4QNILlnMp+e+BTlkhKi0EA/Sn25kZyLpae6J4X0QQgfsRmz\nCTMkoddp/Ghw4az6TX4HNq4bETkCnU7hWNlhL07MA66sifRBCB9auXIlCxcu5IEHHmDIkCGsWrWK\n2NhYXnvttU6bkwQQQoguo6USpk+Pf0rfHn25JvIa30/i6HrwC4SkGxsdvn3A7RwvPc6hkkONjocF\nmij15UZyDQ2aAQUHoPS0NuOJbqPaXo3TL49o/0HaD+4KIDrgmii1kfpU+aE2zvQy17ylD0L4iNVq\nJSMjg9TU1EbHU1NT2bZtWyfNCoydNrIQQlzCVcLUcBWm7AvZ7C7czcOjH0bXgW8oPaIoaqNyvyng\nZ2700vTE6byQ/gKfHv+UYT3r18gPt5h8v4yry6CZsOFpdY7XLtZmTNEt7C86iE7nJC6gkwKIATd1\n6BIxwWE4aiM5U3XUS5PykDuAkAzElejZzw5yKPeipmMOjevBM7M932eluLgYh8NBdHR0o+PR0dFs\n3LjR29PzmGQghBBdRmmVleAAI36G+r+a1matRa/TM7vfbN9PIG8fXDynPqhfooepB1N7T2X9qfXU\n2Gvcx0MD/SivsWPTYgfcnv0gcrCUMQmvy8hXm/P7Bg/WdmB7LVTkt7uB2sXfqEep6U1+zdEmZYY+\nFdAD/EMkgBA+d+kXaIqi+P5LtVZIBkII0WVcuomc3Wln3Yl1TIyfSFRglO8ncHS92qg88OZmX759\nwO2sP7We/+T8h5lJapDhmm9ZlY3IYH/fz3HQDNi2CqrLwBzq+/FEt5BZtB+nNZyowPY3MrfLxVz1\nZwdLmHQ6HUZbH2qVDM5VnKNXcMeud1lkL4gr1uVkAjpLREQEBoOB/Pz8RscLCwubZCW0JBkIIUSX\nUVpla9T/sC13G4XVhdzeX4PmaVADiITxLa4GMy5mHHGWOD498an7mGu+mizlCmpzt9MOJzovdS2u\nPodK9uOoTsDir/H3ih1cwrWhQKe6elRmUWaHr3VZQhOkB0L4jMlkIiUlhbS0tEbH09LSmDBhQifN\nSgIIIUQXUlppJbxB/8M/T/yTMP8wbux1Yyvv8pLqUsjfD/1brsXW6/Tc1v82duTtILdC/ebUteld\niVaN1PEpYA6Dk5u0GU9c9fIr8ympLcJRnUCQ5gFEx3ahbijYkIAeE5nFGgcQIb2gTAII4TvLli3j\nnXfe4a233uLw4cMsXbqU3NxcFi/uvF44CSCEEF1GaZWVsLoH8tKaUr4+8zWz+s3Cz+DXxju9oKBu\n9ZbY1nfhvbX/rYDamwH1Dd+aLOUK6t4U0clQqPFqM+Kqtb94PwCO6t6dl4HoEd/hSwX5+2NW+rK/\naH+Hr3VZQnpBTRnUlms7rug25s2bxyuvvMKKFSu45ppr2Lp1K+vXr6dPnz6dNicJIIQQXUZppdVd\nEvTFyS+wO+3alS+5HsijhrZ6WlxQHONjx7P2xFqcipOwuh4IzVZiAogeBoVHwKlB47a46mUWZWLQ\n+eGsjcPib9B28Atn1F3f/QI6fKkgfyMmWx8OlxzG6tDwfnTvBXFOuzFFt7NkyRKys7Opra0lIyOD\nSZMmdep8JIAQQnQJtXYHlVYH4RY/FEXhkxOfkNwzmQFhA7SZQMFBCAiFHnFtnnp7/9s5V3GO9Px0\ndwmT5gGErRLKsrUbU1y1MosyiQlIAsXYCSVMHd8DwsXib4DavticNo6UHPHKNT0iS7mKbkgCCCFE\nl1BW5doDwsShkkMcLz3Obf1v024CBQfVB3MPlsWb0nsKwX7BfHriU8wmA/5GvXabyQFE1a0cUnBQ\nuzHFVcnmtHHo/CFi6jaQ65QSptCON1CDOndblXotTRup3RkI6YMQ3YcEEEKILsH1DX64xcQ/j/8T\nf4M/M5JmaDO4okDh4TbLl1wCjAHMTJrJxtMbKbeW120mp1EPBEDUYEBX37chRDudKD1BjaOGMGN/\nAG0zEIpSl4HwTgAR5G+kusZCdGC0to3UwTGgM0gGQnQrEkAIIboE1y7UlgCFL059wdTeU+lh6qHN\n4GU5YC2HaM8CCFDLmGodtXx56ktCA03aLeMKYLJAWF8olAyE6BjXN/XBJGHQ6/A3avhYUFUCtiov\nljAZqay1MyJyhLYZCL1BbQKXDIToRiSAEEJ0Ca4MxNnqfZRby5mVNEu7wV0N1NHJHr9laM+hJIYk\nsiF7A+EWP+2WcXWJHiYZCNFhmcWZhAeEo7P3xGIyaLuzrReXcAU1A2FzKAwNT+ZcxTnOV5/3ynU9\nIpvJiW5GAgghRJfgCiB2n/+GYL9gro29VrvBCw6oP6OGePwWnU7HTb1vIr0gnUBzjbuHQzPRw6Ak\nC2zV2o4rriqZRZmMiBhBpdXROQ3U4L0MhEldQap/iNoj5FqeVhMhvSQDIboVCSCEEF2C2oTsYHv+\nFr7T+zva7P3gUnAIQnuDf/BlvS21bypOxUmNXyYlWpYwgdqvoTihSMPVZsRV5ULtBbIvZjM8cjiV\ntXYCr+BdqKG+ATzePACjzsi+on1eua5HQnrBxVxwOrQbU4hOJAGEEKJLKK2yYQk5xUXrRW7q3fJu\n0D5ReKh+ZaPLMChsEL2CelHkTOdCtQ2HU/HB5FoQ7VqJScqYRPtkFGQAMDpqNBW19k5YgekMGM0Q\n2NMrl3NlUOwOI0N7DnV/Pk2EJoDTDhUF2o0pRCeSAEII0SWUVlrxDz1IoDGQCfETtBvYXgvFx+sf\nyC+DTqdjWp9p5NXuR9FVcaFawzKm8CQwBsiO1KLdMgoyMOlN7gxEkOabyNXtAeGlvgtXAFRZaycl\nJoX9xfupsdd45dptci/lKn0QonuQAEII0SWUVNXgCNjPjb1uxN/gr93ARUdBcVzWCkwNTeszDScO\njMGHtd1MTm+AyMGyF4Rot10FuxgeORx/gz+VtQ4spit3EzmoDyAqau2MiR6D3WnXbjUm92Zy0gch\nugePA4jVq1eTmJhIQEAAKSkpbNmypcVzP/nkE1JTU4mMjCQ4OJjx48ezbt06r0xYCHF1yqs9hFNf\nwU19OqF8CdpVwgSQHJFMmCkKY/ABbZdyhbqVmCSAEJevwlrBkZIjjIkeo/6+1t4JTdRnvBpABLkz\nEA5GRY1Ch067MqYe8erPMgkghPdt3ryZOXPmEB8fj06n45133mn0uqIoLF++nLi4OMxmM5MnT+bg\nQd/+2+BRAPHhhx+ydOlSnnrqKfbs2cOECROYMWMGOTk5zZ7/zTffMGXKFL744gv27NnDzJkzuf32\n21sNOoQQ3dt5ZRd6TEyMn6jtwAUHwWCCnv3b9XadTsf46BsxWo6Te/GClyfXhqihUFkIlcXajiuu\neHsK9+BUnKREpwBQadW4B8Jeq/YLeKmBGsBSV4JVWWsn2BTM4PDB7CrY5bXrtyqgBwSESAmT8ImK\nigqSk5N59dVXMZvNTV5/4YUXePnll1m1ahXp6elERUUxbdo0ysvLfTYnjwKIlStXsnDhQh544AGG\nDBnCqlWriI2N5bXXXmv2/FdffZUnn3yScePG0b9/f5555hlSUlL45z//6dXJCyGuDk7FSa1pHzF+\n1xDoF6jt4IWHIHIQGNr/8DQ14SZ0ejvphd96cWIecJVdSRZCXKZdBbsw6oyMjBwJqA/dmgYQF8+p\nP32QgaiotQOQEp3CvqJ9WB0aZQZDEiSAED4xc+ZMfvOb3zB37lz0+saP7oqi8Morr/Dkk09y5513\nkpyczLvvvkt5eTkffPCBz+bU5t8WVquVjIwMHn300UbHU1NT2bZtm8cDlZeXExYWdvkz7ARr954j\n74JGjVftFGAtIfbifq6NNxJiQl39wWFXfzrtQAurwej0oPdT66cNfqA31n372g9iRqjHhNDY7oK9\nYLzIwCANm6ddCg5C4o0dusSEhDE47cFklmwBvu+deXnCtfFd4SFI6thnEN1LRkEGQyOGEugXSK3d\ngc2haNtE7XrQDvVmBqK+iRpgTPQY/u/w/3Hw/EFGRY3y2jgtkgBCdIJTp06Rn59Pamqq+5jZbGbS\npEls27aNBx980CfjthlAFBcX43A4iI6ObnQ8OjqajRs3ejTIn/70J86ePcv8+fObfX3NmjWsWbMG\ngKKiIo+u6St5F6pZ+re9nTqHS+lw0k+Xyxj9Mcboj5GiO0qivm6pOG/uk+MXCPEpkDAeel8LvcaC\nOdSLA4iuqrPvwS+y/o3iNDAi/DptB64qgfK8djdQuwT7++GsGEa2MYNqezVmY9MUs08ERUFghGQg\nrgJa3oNVtioOFh9kwbAFgNozAGibgfDyJnIAfgY9JqOeCqsaQIyOHg3ArvxdGgUQvSDnv74fR3jP\nl09CvoYbDgLEDIcZz3vtcvn5+QDNPqefO3fOa+NcyuO/LS7d3l5RFI+2vP/444957LHH+Nvf/kaf\nPn2aPWfRokUsWrQIgDFjxng6JZ/IKqwE4J37xzI+0fO1qRVFodJWQUF1AYVVhRRWFVBUXYjN2fyy\njmH+YUQFRhNljiYqMIqeAREY9M18+1NzAf93UtGXHFfHMffEmTAeW69xPLY9AHN4PL+dO6ouk1CX\nWdAb1UxD00mqG0+5shQOm/rTXqvuxHtmB+Rsh62/V1elQQc3PwfXPeTxn4O4MnXmPagoCpvOfoWj\ncgDRwRoHrK4G6nYs4dqQTqfDbBuNje18e+5bbRvBo4dKAHEV0PIezCzOxK7Y3Q3Urm/sOyWAcDUf\ne4nFZHB/nrCAMPqH9iejIIMHeMCr4zQrpBfUlEFt+WVvSilER7X3Ob292vzbIiIiAoPB4I5wXAoL\nC5tEO5f6+OOPmT9/Pu+99x5z5szp2Ew1crK4AoAhsT0wm9pO5+4v2s/z6c9zovQEVfaqJq8bdE2v\noaDgVJxNzosMjGTugLn8YPgPMOrr/qdJew5Ks2DmS5D0HXQ9+2HQ6TAANaczyCws904KOHIgJN+h\n/ndtBZzLgG9fhY3PwsDpaomTED5w8PxBimsKsJXfQHigSdvBXQ/e7VyBqaEIw2CKCGLD6Q3aBhBR\nw2D3u+B0gl5W5hZt25W/C71O7/5W3tUzoOkqTBfOQFA0GL27ZLPF3+jOqIDaB/FZ1mfYnfb6f1d9\nxb2U6zmIGuzbsYR3eDET0FliYmIANRORkFD/POjJc3pHtHk3mUwmUlJSSEtL46677nIfT0tL4847\n72zxfR999BH33Xcf7777LnPnzvXObDVwsqgSi8lAVHDrf6nZnDbe2PcGb+1/iwhzBHcMuIMYSwzR\ngdFEW6KJDowm0hyJXzM9BYqicKH2AgVVBRRUFZBfmU9+ZT6HSw7zx71/5Juz3/DcxOdIrCiB9D/D\n+AdhXNNvT5IiLWw8XIDN4cTP4MUHB/8gtZ46chD8cSysfxS+/4nXNvsRoqG002noMWAvH0pooMY9\nOAUHwRwGwTEdvlRYYABV9pFsPrsZq8OKyaBRMBQ9FGxVUHpKAn3hkYyCDAaHDybIFAR0UgaizLtL\nuLoE+RvdARHAmJgxfHj0Q46UHCE5Itnr4zXi3kzujAQQQjOJiYnExMSQlpbG2LFjAaipqWHLli28\n+OKLPhvXo78tli1bxvz58xk3bhzXX389r7/+Orm5uSxevBiABQvUOsr33nsPgL/97W/Mnz+fl156\niUmTJrmzFyaTifDwcF98Dq/JKqogKTKo1bRPVlkWP9vyMw6XHGZOvzk8Oe5Jgk2epyt1Oh2hAaGE\nBoQyKHxQo9f+lf0vVmxfwd2f3c3DNTruCYpG/52fN3udpMgg7E6FMyVVJEUGeTy+x4JjYMrT8OXj\ncPATSG45YBSiPRRFYePpjfS1jGSfM5Bwi8YZiMJD6jf4XgiOwy0mcktHUmn8lv/m/pcbEzRqanaV\nXxUekgBCtKnWUUtmUSbzBs9zH6vPQGjcRN3B3qPmqBmIBgFEXZnWrvxdGgQQspmc8I2KigpOnDgB\ngNPpJCcnh7179xIeHk7v3r15+OGHee655xg8eDADBw5kxYoVBAUFce+99/psTh59bT1v3jxeeeUV\nVqxYwTXXXMPWrVtZv369u6chJyen0Z4Qr7/+Ona7nYcffpjY2Fj3rzvuuMM3n8KLThZVkhRpafY1\np+Lk3YPvcvdnd5Nfmc8rk1/huYnPXVbw0Jbpfafz6ZxPGRsQzfN+1SxKGkS+o2lpFOCe58miSq+N\n38TYH0LsSPjXU1Bz0XfjiG7pWOkxcspzSPAfD0CYliVMTicUHu5w/4NLaKCJqgt9CfYLZsPpDV65\npkcihwA66YMQHtlftB+r0+p+sAaosmrcRK0odbtQe28FJheLv5FKa30JU4Q5gr49+mqzH0RwjNqD\nKJvJCS/btWsXo0aNYtSoUVRXV/PMM88watQofvnLXwLw+OOPs2zZMh566CHGjBlDXl4eGzZsIDjY\nd704Hv9tsWTJEpYsWdLsa5s2bWr191eKGpuD3AvVJEY0TatW26v58Vc/Zkf+Dr6T8B1+ed0viTBH\n+GQekQ4Hfzq+j4/jBvBCdT53rL2Dlya/xIS4xktcJkXUBRDFFYCP6tz0Bpj1e3hzKnz9HMz4nW/G\nEd1S2uk09Do94brRBPiVetR35DVlp8Fa4bVvQcMtfpRVKdydcCObzmzC5rThp9egJMsUCOGJEkAI\nj7h2Zh4dNdp9zJWBsJg0CiBKs8Fe7ZOMWZC/gdyy6kbHUqJT2JC9AYfT0fxiJd6iN0B4EhQd8d0Y\noluaPHkyitLC8vyolS3Lly9n+fLlms1JOu4aOFVciaLQpBxIURRWbF/BzvydPHPdM7z6nVd9FjwA\n8O+n0NlrmTvrTT6e8zHRlmge++YxcityG50WGmgi3GLybQYC1KVdx/4Adq6B3K61xK24sm08vZGU\n6BSqq83aZh+gfgUmLzRQg5o9cTgVJsZO5aL1Iul56V65rkeihtZ/HiFasatgFwPCBhAaUL/iWaXW\nTdS5e9SfcaNbP68dLKbGJUygBhDltnKOlx33+nhNxI2q/3xCXMUkgGjgVLH6IO76Zt/l0xOfsi5r\nHQ+OfJC5A+f6dFkssv4DBz6GG5ZBz34kBCfwh+/8Aafi5JFNjzTZUTMpwuL7AAJgyi/U9ea/WAZO\nR9vnC9GGY6XHyLqQxU29b6K0ykqo5iswuQII7zQ7uuY/IHg0Fj8LX2Z/6ZXreiQ6GUpOgrX5ckch\nQF38Y1/RvkblS9AJTdS5u8Hgrwa+Xma5pIkaYGyM2ljqyr74VNxodW+Zi3m+H0uITiQBRAMni9Ql\nXBv2QBwpOcJz25/j2thrWTxisW8nYKuBLx5VU6DXP+w+nNAjgRXXr+DA+QO8mN64oz4p0sLJYg0C\nCHOouifEuQzIeMf344mr3udZn2PUGZmeOJ3SKhvhFo1XYCo8CGF9vbZeu2v+lbU6pvWZRtrpNKrt\n1W28y0uih6p7vEjphGjFofOHqLZXkxKd0uh4Ra0DU90mbJrI3QsxyWD0/pcGQXVN1A3LPWIsMcQH\nxbMrX4M+iLi6DeskCyGuchJANHCyqJLYkAAC6+pAy63lLNu0jFD/UJ6/4Xnf1k6Cuu9CSRbc8jL4\nBTR6aWqfqdw39D7+dvRvfHmq/pvNpMggiitquVjT/IZ1XjX8LkicBF89CxWFvh9PXLUcTgefn/yc\nib0mEh4QTmllZ2QgDnqtfAnqMxClVVbm9JtDpa2Sr3O+9tr1WxXVYCUmIVrg+gb+0gCistaORasV\nmJxONYCI883O0BZ/I04FamyN91pKiU4hoyCj1Tpyr4gZDjqDBBDiqicBRANZxfUrMCmKwi++/QW5\nFbm8NPklepo935W6XapKYOtKGHYH9JvS7ClLU5YyKmoUz2x7hpNlJ4EGjdRalDHpdHDLSrVMYstK\n348nrlo78nZQVF3EnH7qBpOlVVZtN5Gz1cD5LK8uI+maf2mljZToFGItsaw7uc5r12998EQwmuvL\nsoRoxq78XfTt0bdJD58aQGhUvnT+BFjLfdL/APVL0V5axjQmegyltaWcvHDSJ+O6mQIhaohapiXE\nVUwCiDqKonCyqIKkCLWB+r1D7/FVzlf8NOWn7t06ferwOrDXwPVLWzzFT+/Hi5NexGw0s2zTMqps\n9fs/uMqvfC5iAAyeCQf+AQ572+cL0Yx1J9cRbArmxl434nAqXKi2EablJnLFR0FxeLUGO6xBBkKv\n0zMraRb/zf0vRVVFXhujRXqD2stRKCsxieY5nA72FO5hTMyYJq9V1No7oYHadxkIoEkjtavvQ5s+\niGvUz+nrbIcQnUgCiDrFFVbKa+wkRVrYU7iHVzJeYWrvqSwYukCbCWT+HXoOUPdcaEW0JZrnb3ie\nkxdO8uvtvyYhzIxBr9MmA+Ey/C6oLIJTm7QbU1w1Km2VfHX6K2b0nYHJYOJitQ2nAmFabiLn+qY+\n2nsbSwUHGDHodZRWqQsdzO43G6fiZP2p9V4bo1VRwyQDIVp0tPQoFbaKJuVLAJVWDTMQubvBLxAi\nB7V9bju4PselGYhewb2IMkdp1AcxGqrOQ1lO2+cKcYWSAKKO6xv86FAnj37zKLFBsfz6+l/7dsUl\nlwtn4fS3MOJuj3bEvS7uOpZcs4TPT37O+ux1JISZ6/aC0MiAVPAPgf3/0G5McdVIO51GjaOG2f1m\nA7gfuDVdxrXggLoKTHiS1y6p1+sINftRWqX2IyWGJDIiYgTrsjQqY4oeCpWFUKFBxkNccVwPzpeu\nwARqE7V2AcQe9YsyH/UUBrWQgdDpdKTEpLCrYJfv+yCkkVp0AxJA1HEt4bqx4C3OV5/nxRtf9OoO\n06068DGgQPKdHr9l0YhFjI0ZywvpL9Ar0qZtBsLoD0PnwOHPZNlIcdk+z/qc3sG9GRmpZtvcAYSW\nGYjCQ+o3oAbvPjSFWUyUVtYvtTyr3yyOlR7jaMlRr47TLFc5lpQxiWZkFGTQK6gXMZaYJq9V1trd\nvQM+5bBDXqbPypegQQmTtWmJ7ZjoMRRVF3Gm3Mc7RUcPA72fBBDiqiYBRJ2TxZX49zhB2pnPuT/5\nfob19N7qLG3a/3eIH3NZu3LqdXqeve5Z7E47RaYPOFVcgdOpYb3l8LvUXXyP/Uu7McUVL68ij535\nO5nVb5Y7u1daqX5jr2kPRMEh9R95LwsL9HMHRADT+07HqDfyWdZnXh+rCdfnkTImcQmn4mR34e5m\ny5egrolai12oi46oO1D7qIEaGjZRN92vyJV92VXg4zImo7+6TK00UourmAQQdY4XFWOO+YTEkEQW\nj/Txfg8NFR6B/P3qA/llSuiRwP+O+l9ybRk4AvdwrkyjNecB+k6E4Fg1+BHCQ1+c+gIFhVlJs9zH\nSrQuYSo9DRX5bfYbtUdooMkdEAGEBYQxKX4SX5z6ArvTx4sOBEVBcByc2e7bccQVZ0/hHspqy7g2\n7tpmX6/QahUmHzdQQ8tN1KCWFUYFRmmzvHLcKMjdpy5bK0QHbd68mTlz5hAfH49Op+Odd95xv2az\n2XjiiScYMWIEFouF2NhY7r33XnJyGvfg5OfnM3/+fGJiYrBYLIwcOZK//OUv7Z6TBBB1DlZ9iMNQ\nyrMTnsXf4K/dwPv/Djo9JN/Rrrd/f8j3SQwegn/0Z2TmnfPy5FqhN6glV8fT1CVohWiDoiisy1rH\n6KjRJAQnuI+XaV3CdLSuqXlAqtcvHR5oapSBAJjTbw7F1cVsz9PgwX5gKpz4Cuy1vh9LXDHWnlhL\noDGQKQlNlwhXFKWuhEmLAGI3+Pfwau/RpVoLIHQ6Hbck3cKWc1sori722RwANYCovaDuEC9EB1VU\nVJCcnMyrr76K2Wxu9FpVVRW7d+/m5z//Obt372bt2rWcOXOG6dOnY7fX3wcLFizg8OHDrF27lv37\n97NgwQLmz5/P5s2b2zUnCSCA9LwMqsybGRw4XZslW10URQ0gkiar3x62g0Fv4Onxz6Az1PD2kd97\ndXptGn4XOG1waK2244or0sHzBzl14ZR77weXkkobfgYdFpNGG1kdXQ8Rgy6rZNBToRa1hKlhk+YN\nvW4gxD9Em2bqQTPV0sLsLb4fS1wRqu3VbDi9gWl9phHoF9jk9RqbE6eCdhmIuGtA77tHD1cp1qWr\nMLnc2u9WHIqD9Sd9vDqaq0xL+iCEF8ycOZPf/OY3zJ07F/0l909ISAhpaWnMmzePQYMGMW7cON54\n4w0OHz7M4cOH3edt27aNhx56iPHjx5OUlMQjjzxCQkICO3fubNecun0AUeuo5Rff/hLFFsrtfR7Q\ndvCz6VB2Gobf3aHLjI0biq70Jo5WbNFu51tQS0B6DpDVmIRH1mWtw6Q3kdq38Tf/ZVVWwgJN2qx4\nVl0K2d+qe5n4QHigCVPk/yEAACAASURBVJtDodJaX39tMpiY3nc6/8n5DxVWH6+WlnijukTmEY2W\njhVd3lc5X1Fpq+TW/rc2+7rrQdvnO1HbayH/gE/LlwAMeh1mP0OzGQiAfqH9SO6Z7PuAPnKwurmj\n9EGITnDx4kUAwsLC3McmTpzIRx99xPnz53E6naxdu5aioiJuuummdo2h0bptXdfr+17nXGUONfk/\nYMjNEW2/wZsyPwJjAAy+pUOX0el0JPrNIk85wIrtK0iJSaGHqYeXJtnqwOrSs18/py5FG9LL92OK\nK5LNYePLU18ypfeUJqubldYFEJo4vlHdQG5Qx+65lrg3k6u0NioJmdNvDh8e/ZC002ncPuB2n4wN\ngF+AupP90S/hlpc9WhZaXN3WnVhHfFB8qw3UgO+bqAsOqhlrHzZQu1j8jc02UbvM6T+H3+z4DUdL\njjIo3Df7UWAwQuwIyUB0cb/b+TuOlBzRdMzB4YN5YtwTPru+1WrlkUceYfbs2fTqVf9c9tFHH/Hd\n736XiIgIjEYj/v7+/PWvf+Waa65p1zjdOgNx6Pwh3j7wNkOCpuKoHODehVoTDhsc/BQGzYCAjj/s\n94sMRV88j+KaYlbuWumFCXrItfTsgY+1G1Nccbae20pZbZl774eGSitthFk0WoHp6BdgiYL45h+m\nOsrVx3FpH8TwiOH07dGXz05qsBrT4FugPBfy9vp+LNGl5Vfmsz1vO7P7zUava/6f+/oMhI8DCA0a\nqF2C/FvOQADM6DsDo97I2iwfl9/GjYK8feBsOZgRwpvsdjvf//73KSsr4+2332702tNPP01xcTEb\nN25k165dPPbYYyxYsIB9+/a1a6xum4GwOWw8s+0ZwgLCSFDmkWWpIETLZSRPboKq4natvtScxAgL\nn+6JYsmkBbx/+B1u7nsz18Vd55Vrt6pnP/VhLPPvcP1S348nrkifnfyM8IBwJsRNaPJaaZWV/lEa\nBO92q5qBSL7dZzXYrqVoXZvJueh0Omb3m82qPavIrcglLijOJ+MDMOBmdWGGI+s1eVgTXdfnJz9H\nQWFO0pwWz3E9aPu8iTp3N5jDIbS3b8dBDYZaCyBCA0KZ3GsyX5z8gp+m/BQ/vY/+7Y8bBTteh6Kj\n6kaPosvxZSZAa3a7nXvuuYf9+/ezadMmevbs6X4tKyuLVatWsXfvXkaOVFcgHDlyJFu2bGHVqlW8\n9dZblz1et81A/GHPHzhScoRfXPsLzhRDUqRF2wns/zsEhEL/aV65nGv+02Ln07dHX57e+jQlNRqt\njjT8bijYD4WH2z5XdDtFVUVsOrOJmYkzMeqbPqSUVlkJ1aKEKXsLWMvVRmMfCW1QwnSpW5LUsqmP\nj/s4W2fpCQnXqmVMottSFIW1J9aqq571SGjxPNeGaz7vgcjdC/GjNSmrs5iMLTZRu8zpN4eSmhK+\nPfet7yYijdRCIzabjXnz5pGZmcnXX39NTEzjDSOrqtRNfw2Gxve5wWDA2c6lhrtlALHl7BbeOfgO\n8wbNY0rvKZwsrtC2fMlaCYc/h6G3gtE7D06u+Z8tsfPijS9SVlvG01ufbrQajM8Mu139xlP2hBDN\n+OPeP6KgcO/ge5u8pigKpVU2wrUoYTr6pdpgnDTZZ0OEt1DCBBAfFE9qn1TeP/Q+RVVFPpsDoDaJ\nF+xX97wQ3dL+4v1kX8xusXnaxdUr4NMMhLVK/YJJo4yYxd/Q7E7UDU3sNZHwgHDfNlP37A+mIGmk\nFh1WUVHB3r172bt3L06nk5ycHPbu3UtOTg52u5277rqL7du389e//hWdTkd+fj75+flUV6v7gw0e\nPJj+/fuzZMkSdu7cSVZW1v9v797joqrz/4G/zgyDAzOAKMjFFQW1zMQb5LXULktiWX63b4+2WrXc\nTLO+eck2c1u1u+1q+/3miq5ZsLZfq6+2faXVbMkLgZC/n4qCoabgXREQEBhuc/l8/zjMKDDAAefM\nILyejwcP4MyZcz7zecx75rzP54bVq1cjJSUF//Zv7RuX1+USiMKqQvw+/fcYGDgQi2MX41q1GcWV\nde5tgTjxLWA2yQOQXSQySC5/fpEJg3oMwiuxryDtYho+y/3MZedoll+IfFGWs0Wempao3omSE/j6\n5Nd4ctCTTu+CltdYYLUJ9QdRCyHHXf/7AJ1P6/u3U4CPDpLkvAUCABaMXACzzYy/HP6LamUAcL2V\nhSvFd1nJecnQa/WI69vyeicmd4yBKMiRJy9wWwLhBVMLg6gBQKfRYUrkFOw9vxfXaq+pUxCNBggb\nzhYIumkHDhzAiBEjMGLECFRXV2P58uUYMWIEli1bhgsXLmDbtm24dOkSYmJiEBYW5vj58ssvAQA6\nnQ47duxAcHAwpk6diqFDh2LTpk1ITEzE1KlNxyYq0aUSCKvNiqVpS1FjrcGqCaug99Ijv0ieVjEq\n2I0tEDlbAP/eQETT/uDt5eOtRe/uPjhdLL+eJwc9iXv73Is/H/ozfrr6k8vO06zox4Gyc8D59s0n\nTJ2PEAKrD6yGn7cf5gyd43SfMnetQl2QDZRfkCctUJFWIyHAR9dkDIRdH/8+eGrQU/j65Nc4UXJC\nvYL07C+vdXF8u3rnoA6r1lrrmPXM6N3yd5tbEgjHAGr1Z2AC5NaU1rowAcCjAx6F2SbPEKea3iPk\n6Wstzm8qECkxadIkCCGa/CQlJaFfv35OHxNC4JlnnnEcY+DAgfjqq69w5coVmEwmHDlyBDNnzmx3\nmbpUAvHJ0U+wv2A/Xh/1OqK6yyth5heZALhxDMTVPODU9/LsRS4eyBkVbEB+sfx6JEnC2+PfRk99\nT7ya+qr6888Pelie8/r//VXd89AtY9+lfci8nIm5w+YioFuA033sF9qqz8J0fAcACbhtsrrngZwM\nOevCZPf80Ofh5+2H1QdWq9vF8PZ44Ow+oLpMvXNQh7T3/F6U15Xj0f4td18C4LhTr+pCjpcOAcZQ\nwD9MvXPcwNDNC1UKEohBPQbhtsDbsO2UirMxhY8ArLVAYa565yDygC6TQGQVZiHhcALiI+MxbcA0\nx/bTxSZ4aSRE9Gi6QqfLCQFsXyT3wx77kssPHxVkQH6RyXFREtAtAB9M+AAXKy/inf3vqHuxovcH\nxv2HPJ1r/l71zkO3BIvNgtUHVqOPXx/8+vZfN7ufvauP6i0QJ3YAfUYDBvXXegn01bWYQAR0C8Dc\nYXOReTkT6RfT1SvIoIcAm0W+YUFdSnJeMnr59sLosNGt7muqs0Cv08BLq+LlwKUseQC1mxi6ecFU\nZ4XN1vp33qP9H8XRq0eRX5avTmE4kJo6qS6RQFyrvYbXfngNYYYwLBuzrMGKt/nFlYjo4Qudmh+e\ndvaL6/uXyeMGXCwq2IjKWguKKmod22JCYjB32Fxsz9+u/sqb9ywCAiOB7a/Iq45Sl/X1qa9xquyU\nPEWitvnWhVJ3dGEqOy93YVJp9enGAn29UWpy3oXJ7te3/xoRfhFYfWA1LLbW75S2S+8YwBDMbkxd\nTHF1MfZd3IepUVOh1bTeqlBZa1F3AHVNOVB80q1TChvrZ5SqMre+/sKUqCnQSlr11oQI7CfPuMiB\n1NTJdPoEwiZsWJ6xHEVVRfjTxD816Q+aX2RyDEBWVc014Lul8odo7CxVTmF/HXn13bLsno9+HrEh\nsXh3/7vIK8tT5dwA5MGpD60Crp4C9n2k3nmoQzOZTfhL1l8wstdIPBDxQIv7lthbIAwqJhD2gcQq\nrT7dWKCh5S5MAKDT6rAwZiHyruXhHyf/oU5BNFq5y9ap79n/ugvZnr8dVmHFIwOaX/vhRqZai7rj\nHy4fASDcmkDYX09La0HYBfkE4e7ed+Ofef+EVY0F3yRJfu1sgaBOplMnEHXWOrz2w2vYdW4XFsQs\nwJCgIQ0et9kETheb3DP+Yfe7QGUh8NCH8he7CuyvI7+44XgHrUaLlfeshI+XD2Z9N0vdQdUDHgAG\nTwPSVgElKjUJU4f2Sc4nKKkpweLYxQ1a+5wpqzJDq5Hgr1fxAub4dqDnQCBogHrnuEFrXZjs7o+4\nHyN7jcTaw2thMpta3b9dbp8C1JYDZ1XsKkUdhhACyXnJiA6KRlRAlKLnmGotMHi7YwC1O1sg5Nej\nZCA1IK8JUVhdiB8v/6hOgXqPlKexNVerc3wiD+i0CURFXQVe+P4F7DyzE4tiFmHG4BlN9rlYVo1a\ni039GZguZQH//2PgrudU7QcaHuADvU7jGBh+oxBDCBInJ0Kv1ePZnc8i42KGauXA5PcBjRew41VO\n69rFFJgKsCl3E+Ij4xEdHN3q/iVVdejuo2s10Wi3mmvAmXS3dV8C5MXkasw2VNe1fDdTkiQsjl2M\nkpoSfJLziTqFiZokT27AReU6PavNird+fAs/l/6MxwY+pvh5qndhunQICIhwy/gjO3tCpKQFAgAm\n9ZmEnvqeWLZvGU6WnnR9gcJHyOORCo66/tjUZm5ZH6uTaKmuOmUCUVhViGd2PoNDVw7hvbvfw7ND\nnnV6gWKfsShKzS5MNivwz4WAbxBw3xvqnQeARiOhX0+DY2raxqICovDZlM8Q4ReBF3e9iG/yvlGn\nIP7hwL2/l7tO5Ko4uwV1OGuy1kAIgQUjFyjav6yqTt3uS6e+B2xmVVefbqylxeQaiw6ORnxkPDbl\nbkKBqcD1hfH2lde+OL6DyXwnVmutxSupr2Drz1sxO3o2fjXwV4qfa6q1qrcKtRDAxUPyVKZuZGhj\nC4S31hsfx30MAJi5cyYOXjno2gLZB1JfdPFxqc20Wi3M5pbHqNF11dXV0Omcj2NUnEAkJCQgMjIS\ner0eMTExSEtLa3H/1NRUxMTEQK/XIyoqCuvXr29bqdvp9LXTmL5jOs5XnMfa+9diav/mF8hwyxoQ\nBz6VWyAefA/w6a7eeer1DzbidHHz3SF6+fZC4uRExITEYGn6UiQeTVQnGx/1PBAaDex8HaitcP3x\nqUMprCrE71J/h+S8ZPxm8G8QbgxX9LwSUx0CfVWcwvXEt3Ly/ou71DtHI/bXU9LMYnKN2ZOtGd/O\nwK6zu1wfj7fHy2tgFOS49rjUIZTXlWNOyhzsOrcLS0YtwcsjX25Ti55qYyAqC4HPnwTKzgL97nH9\n8VtgdIyBUD6mYWDgQHw25TP01PfEnJQ52H1ut+sK5B8O9IgCdr8NHPwbk3kP6t69O65cuQKbzebp\nonRoQghUVVXh4sWL6NWrl9N9FH1qfPnll5g/fz4SEhJw9913IyEhAfHx8cjNzUVEREST/U+fPo0p\nU6Zg1qxZ+Pvf/4709HTMmzcPwcHBeOwx5U2rbXW48DBe2v0StJIWiZMTcWfPO1vc/3SxCX56LwQZ\nVboDWnEF2PU2EDkRiP53dc7RSFSwATt/KkCdxQZvL+f5oZ+3HxIeSMAb6W/gw4MforCqEK/e9So0\nkgsbpLRewEN/Bj75JbDnfWDye647NnUYZpsZm49tRsLhBFhsFrww7AXMjp6t+PllVWZ1plA21wDZ\nX8gJxJ3TVBt35Ix9RqmyZhaTayzcGI6NcRvx1o9vYcHeBbi7991YOmqp05W72+W2yQAkIOUPwC/f\nBsKGuua45HFFVUWY+/1c5F/Lxx8n/BHxkW1fKFGVLkzH/gl8M1++efTge0Dsb117/FbYW1SUdmGy\nCzeGY1P8Jry460Us3LsQy8Ysw2O3ueCaRZKAGcnA/74AfPOy/Ln0yEeA0fmFGaknKCgIFy5cwIkT\nKi7k2UnodDqEhITA39/f6eOKPjU+/PBDPPPMM5g9W74wWLNmDXbu3Il169bh/fffb7L/+vXrER4e\njjVr1gAA7rjjDuzfvx+rVq1yeQJxvvw89pzfg9QLqTh45SDCjeH46wN/VfTlm19kQlSw0fX9r4WQ\n77r86w3AUg08tFr+AHGDqGADrDaBcyUmDOjl1+x+3lpvrJywEkG+Qfgs9zPsOb8HE38xEZP6TEJs\nSGyLU28q1ucuIGYmsH890G88EHWv3KWCOoWDVw7i3f3v4mTpyXZf9JZW1WHYL1zYMlddKrf6/bge\nMBUCYcOB8cq6U7lKYBu6MNkN7zUc//Pw/8jJ2JEETNs2Db+N/i1mDZkFvZf+5gpkDAZ++SaQ+kfg\nr/fIXZrGz5dvbLjpc4lc72z5WcxJmYOSmhKsvX8txoWPa9dxXNoCUVMO7FwCHP5vIHQo8KsNQK87\nXHPsNmjrIOobBeoDsTFuIxbtXYQVmStQUlOC56Kfu/nrhO595CRi/zrg+zeBhDHA1P8C7mi+lwS5\nnkajcXrjm9qu1U+Nuro6HDx4EIsXL26wPS4uDhkZzgfiZmZmIi4ursG2Bx98EH/7299gNpub7U+l\nhNVmRXZxtpw0nE9F/jV5pp8B3Qfg2SHPYvrg6eih76HoWPlFlRgT1bPdZbleKLM8z/y5/cD5H+Xf\nlfX9mSctBYIG3vw5FIoKkrtj5RW1nEAAgEbS4Hd3/Q5Dg4Zie/52fHXyK2w+vhlGnRHjwsdhUp9J\niAqIgo/OBwYvA3x1vvD18lU0t7jD/cuBn78DvnhKHlgdOhSIGCMv6hUxBvALvZmXSx5QWlOKVQdW\nITkvGWGGMPznvf+J+/rc1+YvWCEESk3m9o+BEAKw1Mgzm1RdBQ4myT91lUD/++svkie4/SLZ3gLR\nlgQCALw0Xphx5wxMjpyMVQdWYd2Rdfgm7xtMjpyMIJ8gBPsEI9g32PF3mxKL8fOBkTPrk6t1wKZH\ngbBh8vZ+9wBeenkaZlfcOOhEhBAQEK5tnXWBs+VnMePbGRBCIPHBRNwZ1HJre3NsNgFTnbV9CYTN\nJsdaXaXc0nA1D/j2Nbm73D2LgYmvAV4qLxDZjLZM4+qMr84Xa+5bgz9k/AEfZX2EbXnb0M+/H/r6\n923w4+/tD51WBy/JS9nnn0YDjH1RTuL/8Tzw5W+AYU8BY+YC3fyAbv6AtxHw6tblk3shBCw2C8w2\nuSXXV8ebjx1Nq58axcXFsFqtCAlpuPBZSEgIvv/e+QqnBQUFeOCBB5rsb7FYUFxcjLCw9i9nn523\nHzMy5kArBIbW2DCvyoIxVVaEnz4CZB2BOfm/cEXhsbYKAb88HfBho2potn+ikAdF28yA1SLPqmAz\ny7/tAiKAyHuuXyCHDGnmWOqwT+X66pYjWJGsdLpWHYBp8JKmQPL+GTX6o0ip+RH/Ovsv57vbdAC0\nADSAkCBBAhr8NCQF9oSuewC8YYYOV6G7uA24+L+AY8Y8CfYaF06e31mIZv62/2+T5HqwOf4HBlsC\nkDh7n7uKqEjRlbP44edteLLCjKfOnILP0dkobOex9noJ+B/WAceai0HR9H9LrZw4WGoaPkfSAkMe\nA8a/LI+/8ZDu9WMg/rTzBNbtbe+6Kw9C7x2JS3XJ2FjxKSA56a8rJMgxWB+L0EASGjQd2tYopnqG\nQN+jO3xRAu3+NyDtb3RYSLd8HLbwCe70fwFASBKsAKwSHL8tkoShdUb89+xMtYraLt1MNowuuoIn\nyswIOj5V8XeeMxndBPwP6ICcFmKw8d/mKjlxaKxHFDDrO6DPqJso0c3z9dZCIwFrdp9CUsaZdh9H\n4H54G7xxoToP56/+jFSvDEBqpmui0ALCC4C2Pg6Bht+JjWLKGzD06Q/fkr2QduxtdDD5u+BWjsPW\nYlDgetzZ/7cBMEuApT727KLrDNg8W6UpdqndFN92aJxdCyFazLid7e9sOwBs2LABGzZsAAAUFRW1\nWI6oHv3xH5URuM1sgC+0gAYwG4Gzil5FQxqNhEGh/oDTGSiaeW0aL/lHq5P7VWt08t/BtwN9xgAB\nvdtREtfx0+vwevwg5DUzE1PrwgFMghA2lNvOolaUwYJqWEUtLKiGRdTAKmpggxWAfHcOsNX/deNF\nTvODxCRhg6+1HEZLKbxEHSQhIMFWf9kiIInmBjfd+gPPpGbeV5r6xyRh/8qRoAEQZlA2l/vNaksM\nhvj/Au+WD4YeWhQG3Nx5NRoJ/q3FoNToC9ir2/U75vbfOh+5i1xg35srkAvotBr8fsodOFl4s5MH\nBAEYByFsqEMlakUZam1l8m9RBitqIWCDgBVCyL/tcWkn0CgRu5EAAiyF6GathgZWSMIKDWzQCGv9\n/86ed+vEYHOxdv3xRr+FVH9bRIIWEjQC0EJCL2PHi0FfH3/8u2UErO387ruR8hi84W+dAehmrL9r\n7iffNdcHAH3HAd5uWFepFZIkYemUO/DzFVdM4HG927UQNtSIUpjEZVTZrsAiqmGDBTZYIGCBTVhg\ng7X+u9B+iWyPQ+exo7dWQm+thFZY5B9YoLHJv+XvRjR6bueIwYaplQQI+bakFhK8hByDXvV/B7kp\nBqltJNHKlB91dXXw9fXF559/jscff9yx/cUXX8TRo0eRmpra5DkTJkxAdHQ01q5d69i2ZcsWPPXU\nU6iqqmqxC1NsbCwOHDjQntdC1CW5OmYYg0Rtwxgk8izGjPu12rHT29sbMTExSElJabA9JSUF48Y5\nH7Q1duzYJt2bUlJSEBsbe1PjH4iIiIiIyLMUjQxbtGgRkpKSsHHjRhw7dgzz58/HpUuXMHfuXADA\njBkzMGPG9ZWe586diwsXLmDBggU4duwYNm7ciKSkpCYDsYmIiIiI6NaiaAzEE088gatXr+Kdd97B\n5cuXMWTIEOzYsQN9+8r9jc+dO9dg/8jISOzYsQMLFy7EunXrEB4ejo8++kjVNSCIiIiIiEh9igdR\nz5s3D/PmzXP62N69e5tsmzhxIg4dOtTughERERERUcfT6iBqdwsKCkK/fv2cPlZUVITg4GD3FugW\nxbpS7lavqzNnzqC4uNhlx2MMugbrSrlbva4Ygx0T60q5W72uXB2D1LoOl0C0hKPslWNdKce6Uo51\npRzrSjnWlXKsK+VYV8qxrqitOtbymkRERERE1KExgSAiIiIiIsW0K1asWOHpQrRFTEyMp4twy2Bd\nKce6Uo51pRzrSjnWlXKsK+VYV8qxrqgtbqkxEERERERE5FnswkRERERERIoxgSAiIiIiIsVuiQQi\nISEBkZGR0Ov1iImJQVpamqeL5HY//PADHnnkEfTu3RuSJCEpKanB40IIrFixAuHh4fDx8cGkSZPw\n008/NdintLQU06dPR0BAAAICAjB9+nSUlZW58VW4x/vvv4+77roL/v7+CA4OxtSpU3H06NEG+7C+\n2oYxyBhsC8ag6zEGGYNtwRgk1YkO7osvvhBeXl5iw4YNIjc3V7z00kvCYDCIs2fPerpobrV9+3bx\n+uuviy1btggfHx+RmJjY4PGVK1cKo9Eotm7dKnJycsTjjz8uwsLCRHl5uWOfyZMni8GDB4t9+/aJ\njIwMMXjwYPHwww+7+ZWoLy4uTnz66aciJydHZGdni2nTpomQkBBx9epVxz6sL+UYgzLGoHKMQddi\nDMoYg8oxBkltHT6BGDVqlHjuuecabBswYIBYsmSJh0rkeQaDocEHp81mE6GhoeKdd95xbKuqqhJG\no1GsX79eCCFEbm6uACDS09Md+6SlpQkA4vjx424ruydUVFQIjUYjkpOThRCsr7ZiDDbFGGwbxuDN\nYQw2xRhsG8YguVqH7sJUV1eHgwcPIi4ursH2uLg4ZGRkeKhUHc/p06dRUFDQoJ58fHwwYcIERz1l\nZmbCaDRi3Lhxjn3Gjx8Pg8HQ6euyoqICNpsNgYGBAFhfbcEYVIbvqZYxBtuPMagM31MtYwySq3Xo\nBKK4uBhWqxUhISENtoeEhKCgoMBDpep47HXRUj0VFBQgODgYkiQ5HpckCb169er0dTl//nwMHz4c\nY8eOBcD6agvGoDJ8T7WMMdh+jEFl+J5qGWOQXM3L0wVQ4sY3LyAP/Gm8jVqvJ2d11tnrctGiRUhP\nT0d6ejq0Wm2Dx1hfyjEGleF7qinGoGswBpXhe6opxiCpoUO3QAQFBUGr1TbJdAsLC5tkzV1ZaGgo\nALRYT6GhoSgsLIS4Yd1AIQSKioo6bV0uXLgQn3/+OXbv3o2oqCjHdtaXcoxBZfieco4xePMYg8rw\nPeUcY5DU0qETCG9vb8TExCAlJaXB9pSUlAZ98rq6yMhIhIaGNqinmpoapKWlOepp7NixqKysRGZm\npmOfzMxMmEymTlmX8+fPx+bNm7F7924MGjSowWOsL+UYg8rwPdUUY9A1GIPK8D3VFGOQVOWmwdrt\n9sUXXwidTic+/vhjkZubK15++WVhMBjEmTNnPF00t6qoqBBZWVkiKytL+Pj4iDfffFNkZWU5pvFb\nuXKl8PPzE1999ZXIyckRTzzxhNPp2IYMGSIyMzNFRkaGGDJkSKecjm3evHnCz89P7Nq1S1y+fNnx\nU1FR4diH9aUcY1DGGFSOMehajEEZY1A5xiCprcMnEEIIsXbtWtG3b1/h7e0tRo4cKVJTUz1dJLfb\ns2ePANDkZ+bMmUIIeUq25cuXi9DQUNGtWzcxYcIEkZOT0+AYV69eFU8//bTw8/MTfn5+4umnnxal\npaUeeDXqclZPAMTy5csd+7C+2oYxyBhsC8ag6zEGGYNtwRgktUlC3NC5jYiIiIiIqAUdegwEERER\nERF1LEwgiIiIiIhIMSYQRERERESkGBMIIiIiIiJSjAkEEREREREpxgSCiIiIiIgUYwJBRERERESK\nMYEgIiIiIiLFmEAQEREREZFiTCCoWUVFRQgLC8Nbb73l2JadnQ29Xo+tW7d6sGREXQNjkMizGINE\nzklCCOHpQlDH9d1332Hq1KlITU3F8OHDERsbi1GjRiExMdHTRSPqEhiDRJ7FGCRqigkEtWrBggVI\nTk7GxIkTkZaWhsOHD8NoNHq6WERdBmOQyLMYg0QNMYGgVtXW1mLYsGE4efIkMjIyMHr0aE8XiahL\nYQwSeRZjkKghjoGgVp05cwbnz5+HJEnIz8/3dHGIuhzGIJFnMQaJGmILBLXIbDZj7NixGDhwIEaP\nHo0VK1YgOzsbERERni4aUZfAGCTyLMYgUVNMIKhFS5YswebNm5GdnY2AgADEx8ejuroae/bsgUbD\nBiwitTEGiTyLRwP6xwAAAJFJREFUMUjUFN/51KzU1FSsXr0amzZtQvfu3SFJEpKSknDs2DF88MEH\nni4eUafHGCTyLMYgkXNsgSAiIiIiIsXYAkFERERERIoxgSAiIiIiIsWYQBARERERkWJMIIiIiIiI\nSDEmEEREREREpBgTCCIiIiIiUowJBBERERERKcYEgoiIiIiIFGMCQUREREREiv0fvp01djHIbgEA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1107.12x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dr_2nd = wrap_as_xarray(integrated_2nd)\n",
    "dr_2nd.isel(time=[0, 10, 128], sample=[4, 10, 16]).plot(col='sample', hue='time')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lXuBaAopEyh2"
   },
   "source": [
    "# Run untrained neural net model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 53
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 328,
     "status": "ok",
     "timestamp": 1564033396293,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "bUEzHx8wE4VE",
    "outputId": "913b6128-d4b2-48bd-80ef-45fc9dfd92d6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'concentration_edge_x', 'concentration_edge_y'},\n",
       " {'concentration', 'x_velocity', 'y_velocity'})"
      ]
     },
     "execution_count": 17,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_nn = models.PseudoLinearModel(\n",
    "    advection_equations.FiniteVolumeAdvection(0.5), \n",
    "    coarse_grid,\n",
    "    num_time_steps=4,  # multi-step loss function\n",
    "    stencil_size=3, kernel_size=(3, 1), num_layers=4, filters=32,\n",
    "    constrained_accuracy_order=1, \n",
    "    learned_keys = {'concentration_edge_x', 'concentration_edge_y'},  # finite volume view, use edge concentration\n",
    "    activation='relu',\n",
    ")\n",
    "\n",
    "model_nn.learned_keys, model_nn.fixed_keys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 53
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2765,
     "status": "ok",
     "timestamp": 1564033399165,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "ongs9-eHd-lV",
    "outputId": "21db40c8-1558-4cf1-f5f0-853ab4fef9c3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.17 s, sys: 112 ms, total: 2.29 s\n",
      "Wall time: 2.22 s\n"
     ]
    }
   ],
   "source": [
    "tf.random.set_random_seed(0)\n",
    "\n",
    "%time integrated_untrained = integrate.integrate_steps(model_nn, initial_state, time_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 236
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 942,
     "status": "ok",
     "timestamp": 1564033400207,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "DU_31kVfeKBB",
    "outputId": "cad8a412-5417-4963-cfe0-a0837b33f687"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.plot.facetgrid.FacetGrid at 0x7f201a7e30f0>"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TsRLZzXYcZkdZjkGL20YoniaXU1QrkdlEIL+YqRVJkgjYA4wlhZ1BYBzRTLSo\nw7ff7kcmVpJjMADezoaNIZ01JmJgt5iwmNXdYKfVCXY/JMNl11eLHjEQCcgzluHhYRYsWIDLNXW1\nudmKJEm4XC4WLFjA8PBwxXOEMBAAExWJtB4GlVjetFwIA8FBIZKOoKAwHJ/44ApWEgaZJITehlZj\nKxJBvlzpNKxEoCZrlgqDgMtGTslboFytjJlMNFWx8JmMgCMgrEQCQykVwT67j6wUw23LR+EySUiE\nGmolqjZioAkZrTmbhiRJOO1Z9RyLC7wdan5EnbQ4W7CYLKKXwQwmk8ngdNa3OTNbcDqdk9qphDCY\ngTw/9Dxfe+ZrhiYC94X7MEtmFnkn92n3BHoYTgyXLYAEAqPRFr4j8RGyOfWPfCifyBsoFAbBXkBp\nSMRgulWJQF1IlVqJNAETjKUZtznJSRIBpf6P3CZHk7ASCQylNNHeb/ODJOO05//GaAvrOkqV7ovt\n46ubvjpp2etMNmNIxADAbpOBvDDwzZ8otVoHJslEh6tDCIMZzlyNFJRyoP8OQhjMQB7uf5jf7vgt\nmwc2G3bP/kg/CzwLDlgVYnlAXXztCO0w7LkCQSU0YZBVsgST6iJYzzEoTD5uUKlSOSeTyqaK7BUH\nomLEoEAYBK3q9025+ksdNtubhZVIYCilEQMtod5qzS+6DRAGzw09xwO9D0wadc7kqhMGVpMVi8ky\niTBQd0JdVhf4FqrCwIAyo0IYCOYCQhjMQAai6u7HL7b+YnoXvHIvvPiTA57SH+mfNPFYQwgDwcGi\nsCSgZicKxdI4rCactoIk49H8IqNlmaHP18s3TtNK5Lf7yyMGrglhMJZvEhXIynWPTViJBEZTKgw8\nVjUh0WzN7+4bIAy0Bbwm9EtJZ9NVWYlAjRpUEgZWq6y/jm8+ZGJggJjudHcW5T0JBBr9/f1IksQL\nL7xwqIdSN0IYzEAGogNISGzau4n+cP+BT87l4NGb4KnbJj9FybE7srtiD4NC2pxt+O1+kWcgaDiF\niwftD3EwlqHFbS8+cXQH+A8D2/QW8NNFW2xM20pUIWLQ7FEXOaF4mhDqbmUgnap7bE2OJsYz43qn\nWIGgXmKZGG7LxHvdbvIAYDLn/fuRvDCoI8dgSmFQZblSOIAwsBRGDOarBw2wE2nCQPTzEZx22mn8\n4z/+o/7zokWLGBwc5Oijjz6EozIGIQxmGIqiMBAb4ENLPoTFZOGX23554AsGX4boPhh7e9JazoOx\nQVLZ1JQRA0mS1ATkMSEMBI2lYsQgnibgLlk4jO5oWEUiYNpWogNHDDKMZdRyiYFUrO6xNdubAUSj\nJYFhxDKxove6BVUkSOYCK5G372u3AAAgAElEQVTFCY7ay+1qScL7k/srvl5t8jGoEb1KwsBszoBi\nwmaygX+hetAgYSDnZPYnKv8OgrmL2Wyms7MTi2XmdwEQwmCGEUqFSMgJjmw9kg1dG/jDzj8QTR+g\necv2P098P7Kt4ila1GGqiAGodqKdoZ1ix0TQUELJEE6LE7NkLogYpIubm+VyqpWozfiKRJowmG7E\nwG/3k5ATRbv4TpsZh9WkRgzy1p+mRGSyW0wbrbfCZDuvAkG1lCbamxX1+5wpHzEYH1RLldaRuBmX\n88JgkkV1tcnHMHnEwGxOg2JTEyy1iEH4neoGXIHCXgaCucsVV1zBE088wfe+9z0kSUKSpDIr0caN\nG5Ekif/93/9l7dq1OJ1OTjnlFN555x2eeOIJ1qxZg8fj4eyzz2b//uI5cffdd3P44YfjcDjo6enh\nO9/5DrncwVtzCWEww9DyC+a753PRqouIy3Hu771/8gt2/HmiI+zwmxVPmaqHQSHLA8uJy3F9HAJB\nIwilQrQ4Wmh1tuoRg2AsXVyqNLIXMvGGVSSC6ecY+GyqJzucLrETuWzsj6YZS43hUCScifpzA/Tu\nxymRZyCon2wuS0JO4LF6Jg7m1Pd9lnyEa3xoYoFdI1rEYDJBW0vEwGlx6nO1EMmcRsnl7+XpVLsf\nGxQxANHLYK7z3e9+l/e+971ceeWVDA4OMjg4SDabrXjujTfeyO23386zzz5LKBTiggsu4Otf/zp3\n3XUXGzduZMuWLdx00036+T/60Y/4yle+wte//nW2bt3Krbfeyn/8x39w5513HqTfTgiDGcfeqNqt\nbr5nPqtbV7OmbQ33br238g5+eC8MvQbH/gNYXbCvsjDoC/fhtXppcbRM+fzlTeoiTOQZCBrJWHKM\ngCNAh6tDjxiESoVBgyoSQW1WIoBIqsRO5LHpEYMmyQKxkbrH1uJU52lhjweBoFZ0EVzwXs9kLCg5\nMxklLwwi9Tc3055zoOTjqiMGVieJTHnEACmNkrWpzQXNFlUcGCkMRMRgTuP3+7HZbLhcLjo7O+ns\n7MRsNlc899/+7d845ZRTOOqoo7jmmmvYvHkz3/rWtzjhhBM49thjufzyy3n88ceLzv/mN7/Jeeed\nR3d3N+eccw7XX3+9EAaCydEjBh519+biVReze3w3m/ZuKj95R95GtOJD0LZy8ohBWK1INJ36vlpl\nIpFnIGgkoVRIFQbuDobjw6TlHOMpuaRUaf492ABhoO1uVpN8DOURg4DLplYlSo0RMDsgNlr32BZ5\nFmGWzHpTQoGgHirZ5mLpLErORVqJqmU+x4fqqkgEUycfV1uuFCbPMVCkFErOTjyT38X1zYdI/Vai\nJnsTdrNdCAPBtDnqqKP07zs6OgA48sgji45pHYhHRkbYs2cPn/70p/F4PPq/66+/nt7e3oM25pmf\nJTHH2Bvdi8/mw2vzAvCBxR+g3dnOvVvv5dSFpxafvONhCHSpHuz2w+Gthyvesy/SxwmdJ0zr+W6r\nmwWeBSJiIGgooWSIZU3L8Nq8bB7YzFil5majO8DhB3eb4c+vVhhMGjFw29gdjONOhmiyuCC+H3JZ\nMFXeXZoOVrOVRd5F7BrbVfM9BAKNSsIgmpJRsk6S2XHVricnwN1a13OmshIZWa40RwolZyOalPHY\nLaowmCTHrhokSaLT3SmEgWDaWK0TYlfbfC09puUPaF9/8IMfsG7duoM4ymJExGCGMRAdYIFngf6z\n1WTl4ys+ztMDT7MrXLBQSMeh7wno+aCaMNZxuGpjiBZbGeKZOMPx4SkrEhWyvGm5EAaChjKWGiNg\nD9DuaieWifFORPXTl1mJWnvqSoicjJhcXR+DqSIGoVSIJrsPUMCAPIMl/iXF810gqJGKwiCpCoN4\ndhyS+fe0w1/XczQrUSgZqmh9NbJcaZYkKDaiqXzfEP9C1VprQJOzTlenyDEQYLPZJs0rqJWOjg4W\nLFhAb28vy5YtK/t3sBDCYIYxEB3QbUQa5/Wch9Vk5ZdbC0qX7toIclIVBgDtq9SvI1uLrtUSj6dT\nkUhjeWA5/ZF+0tl0laMXCKYmISdIyAkCDlUYAPQFVQtdoNRK1Gp8RSJQBbOEpDZImgYHihiMJ2VC\nyTGa7WrSsBF5BkualrBnfI/oZSCom4pWopQMWRexTASS+fe0QcIgq2TL5gmo3caNihjISj5ioAkD\nvclZuOzcaulwi+7HAujq6uK5556jv7+f0dFRw6oG3XTTTXzzm9/kO9/5Dtu3b+eNN97gZz/7Gd/4\nxjcMuf90EMJgBqH1MCgVBi3OFjZ0b+D+3vsZT6v10tnxZ7B5YfFJ6s/tR6hfSxKQ9VKlVUQMegI9\nZJWs8DgLGsJYvkOplnwMsCffYKkl3zSMZBiiQw2pSAQTdd2nk3cD6BVdyqoSuW1AlmhmnCZX3vJk\nQJ7BEv8SskqW3eO7676XYG5TyTYXTclIikvtzWFQxCCRSegRgUp2opqSjy1Oktkk2Vzxzm06l4Cc\nTRU4YHiTs9HEKHKu/i7mgpnLF7/4RWw2G4cffjhtbW2YTMYspz/1qU/x3//939xzzz2sWbOGU045\nhbvuuovu7qmrRhqFEAYzCK2HQaGVSOOiVReRkBP8Yecf1PruOx6GZaeDRSvZ1g7O5rIE5P5IPxIS\nh3kPm/Y4tATkHaEdtf8yAsEkaGU4m+xNesRgMKpWJtIjBg1MPAZ1d3O6NiIAs8mM1+atGDGQ8t1j\nA25V5BgSMfAvARB2IgEAv9j6C67967U1XRvNqH1wCjsfR1MyVjxqN2/tPW2vP2Kg/e0qbXKWzWXJ\nKlms5uqFAUAymyw6ns4lUHL2goiBsU3OckqOkXj981gwc+np6eGZZ54hHo+jKApdXV0oisKxxx4L\nqJ2RFUWhtXUiN+e8885DKbGzXXPNNYyOFm8WXXjhhbz00kskk0lCoRCbNm3iE5/4RON/qTxCGMwg\nCnsYlHJEyxEc3XY0v9vxOxh8Rd1N7dkwcYIkQccR5cIg3M98z3wcFse0x3GY7zCsJqvIMxA0BC1i\n0Oxo1oXBcEKt2tDkyi8cGliqFNRd1OkmHmv4bL6KOQaSRbVqNHnzi5N4/V1TtZ4jIgFZAOrfhmcG\nn6np2kqleWMpGbvJQ1yOk4nnd/frjRjICRZ4KwuDTE61xNlM1Xc+1u5dSCqb1JOPgYKIgYFNzkSe\ngWCWIoTBDKK0VGkpJ8w7gb5IH+ntDwESLD+z+IT2VTC8tSgBqz/SX5WNCNSE5yX+JewYExEDgfEE\nU+pCpMnehNPixGfzEUyN4nNYsJrzH1mjO8BkhcDihoxBsxJVg9/unyRioC68ApowMCBi4LK66HR3\nioiBAACvzat23s5Vn3Oief9LrUR2U94epy2AHb6ax5dTciTkBAs96hwIJoqtRNq4a+ljABT1Mshk\nM8iKrFqJ0nlh4O0EJNHLQCCYBg0TBnfeeSfd3d04HA7Wrl3LU089Nem5v//971m/fj1tbW14vV5O\nOOEEHnjggUYNbcYylTBY7FtMTsmxZ+f/wqLjy8vLtR8O6SiMqb7knJKjP9JPt69679rygKhMJGgM\nhTkGAO2udsLpEVo89omTRt+C5iVQpfVgusQysaqsRAB+m79ijoFmJWpytah2PgNyDEC1E4k8HwGg\nl6/Wc8yqIJaJYZEs2M0T8yuaknFZ1HtGtAhXHRGDpKxafTrdnZgkU1mOgVbIopbkY6Co+7H2vZJT\nE/8B9XPC26l2S68TIQwEs52GCIP77ruPa6+9lq985Su8/PLLrFu3jg0bNrB7d+VEuSeeeILTTz+d\nP/3pT7z88st86EMf4mMf+9gBxcRcpLSHQSmavaB/rHeiGlEh7YerX4fVykTD8WEScqKqikQaywPL\nGY4Pqx5UgcBAgskgZsmsv887XB3Es0ECrgIRMLoD2hpjIwLVmlC1lcjuK4sYNLmsExEDe8CwxQlM\nCIOKXc8FcwqtXG6twqA00T6akvFY8yV4E0E1OleF3bQUbbHutXppsjeVCYOaIwZ5YVBoJdKSqc3Y\nJ5KPQbUTheufe16bF7fVLYSBYNbSEGFw2223ccUVV3DVVVexatUq7rjjDubNm8f3v//9iud/97vf\n5frrr+f4449n2bJl3Hjjjaxdu5Y//OEPjRjejGUgNlAx8VhjsU+1VfRZrZMIg5Xq1+Et6nn53cZq\nrUSg9jIARNRAYDhjqTH8dj8mSf14ane1kyI00cMgm4HgroblF0CNViKbX63iUoDVbMLhUBctTfYm\ndcwj2w0ZY7e/m2Q2yWBs0JD7CWYu9QqDUhEcS2UnhEF6TI0W1NEvRFusu6wumh3N5cIgX3a31ohB\noTDQvreZnRPJx5Dvfly/lQjyvQyEMBDMUgzvfJxOp3nxxRf54he/WHR8/fr1bN68edr3GR8fJxAI\nGD08w7nnmX7eGo5OfaKisCj2BqvCT2DNpWp61k7XG3TkHDz7n1cSswR4ueVDhG2dRec05Uy8Zffx\nf5/JgvSGfvx9PW2csaoD/Iv0iEEtPQw0tMpEb429xbGdx9b0+wgEldCam2l0uDvISeP4nfl9jGAf\n5OTGC4MqrUQ+u49wKoyiKEW7rw57EhmXWnGlbQVsfQAyCbBOr0fCZOiVicZ2HXDDQDD70aJrlfoD\nTEUlYTCelNXeHHL+nnXkF8BExMBpcdLiaCm3EuVUK1GtVYmKIgYFzyoWBguhd2O1Q69Ip1s0ORPM\nXgwXBqOjo2SzWTo6OoqOd3R08Oijj07rHt/73vd45513uPTSSyu+ftddd3HXXXcBMDJy6EqGxdMy\n/3r/FpxWMw5r5eBLszLG2TzBR5THWcJeUliJU31IVgFCi5s4KT5GT7APH1HeN/TfbOQ4fil9iBc5\nHAdplnckeM3cxNBrE7uIsVSWzb37VWHQvkrvZdAf7sdlcemVX6qhw9WB1+YVEYM5wsGcc8FkUM8v\nAGh3toOk4HTmfcR6RaLG9DAAdXFRrZXIb/OTVbJl11pscXJK/ue2FaDkYP9O6DyyrjEuaZooWXrK\nwlPqupfg3Uc1c04XBpnahEFpdCyWkgnYWyAG4UzUkIpEoFYRanY082awuDpevVaiohwDLTphcU1U\nJQI1YpDOd3Ku8/fpdHeyNbh16hMFghmI4cJAo7QxUOku2mT87ne/40tf+hK/+tWvWLy4csWRq6++\nmquvvhpArxl7KNg1onqHb/v4GjYcOa/kxY3w7F1qozElC4tOhPf8C/YjPobd7qn6WaFkiMR9p7Lk\nAzcSOPwSGNsDL/wXZ7z4E85I3KQ2MDvsRG7qz9AfMPHyp9fr1/7Hn7fx46d2kcnmsLYfDr2PQzZD\nf6Sfxb7F027iVIgkSSxvEgnIc4WDOefGkmP6ohfAb1OT6C22/KJHEwYtjREGWgWVWnIMAMKpcNG1\nZkscZE0Y5O18I9vrFgbNjmaa7E0iAXmWUs2cqyf5OJ6J47FN/E2SszkSmSwBhw+TZCIsx8HRcYA7\nTO8ZkLcSOZvLqhLpyccGlCudqLLkmqhKBMVNzuoUBh3uDoLJIOlsumr7k0DwbsfwHIPW1lbMZjND\nQ8VhtuHh4bIoQim/+93vuPTSS/nZz37Gueeea/TQDGdn3kK0tL1koR/cBfd8DN55Htb9I3zuefjk\nw3DMpVCDKIAKFYmaFsEHboIvbIVz7wDJBC/8F105EyE5VpQUvLTNQyarsDsYVxOQcxnY30vvWK+e\nsFwLPYEedo7tLGvYIRDUQygVUv34eWzkowcWTRi8Bd559dsbMvEDHq+lKhFQlmegSDGycv5eLcvU\nuWpQnoGoTCQAY3MMYmm1i7DHYVV7c2RTYDfOStTsaGY8M66LAZgQBlVbiSqUK9WjE9aSiIFfa3Jm\nQGWifC+DfbF9dd9LIHi3YbgwsNlsrF27lkceeaTo+COPPMK6desmve7Xv/41l1xyCT/5yU8477zz\njB5WQ+gdiWI2SSxuKVlAbH1QtQtc9Ric+XVDqqfsjaofZmVeYqsTjrkMrnkKrvxfuk76EkDRYmFZ\nXrj0DkehQ61MFBp4jn3xfaxsXlnzmJYHlhPNREXyo8AwckqOcCpcZCWyKOqCOyupZUwZ3VF3fsHL\nwy9z0q9O4u3I22WvaYuYapOPCyMGhchSlHTaqQpoix0C3TCyrcaRF9Pt7xa9DAQ4LU4skqUmYRDN\nRItEsObL9zos+O1+wrl03TvshWK72dEMUJRnUGuDswNVJfLa3OXJx2BIZSK9ZKnIMxDMQhpSlegL\nX/gCP/nJT/jxj3/M1q1bufbaaxkYGOCaa64B4LLLLuOyyy7Tz//Vr37FxRdfzC233MKpp57K0NAQ\nQ0NDBIPByR7xrqB3JMphzS7sFnPxC1sfhHlHQ9Nhhj1LixjM88yrfIIkweJ1LF52FkDRgmdJmzs/\n3pi6oJLMbB94HoAVzStqHlNPQF2cCTuRwCjG0+NklWxR8nEm7ULJmUkRUpvzjb5Vd35BX7gPOSfz\n3NBzZa9V6gQ7HbRd29KIQVoZJ5txkcioO7G0rTQ0YjCWGitL5hTMLSRJwmvz1pR8XNrlWyvx6bZb\n8Nl8RJANyzFwWtXkYyjuflxrjoHVZMVislS0EvntnmJh4J2HaHImmMlU0x+sHhoiDC644AJuv/12\nbr75Zo4++mg2bdrEQw89pOcM7N69u6inwQ9+8ANkWebzn/888+bN0//93d/9XSOGZxg7h6MsbSvx\nIUcGVQvRqnMMfdbe6F68Nq+++JiMhd6FmCWzXnEIwOew0u61q9Ynix1alrE9qO5YrgjULgyWNS0D\n1MpEAoERhJIhAJocE1aisUQGRfYTz+5XG/SlwnWL7rGUGn14dfjVstd0j7KlyuRju7p4KowYJOQE\nspJCyboJxvLWibYeCPaqZVfrRE9AHhNRg7mO1+atOmKgKAoxudhKpDUF89gt+GxewpJSf8RALogY\nOPMRg4I8g1rLlYIaNagUMfDZ3cRS2YkTzVbwdIgmZ4IZSbX9weqhYZ2PP/vZz9Lf308qleLFF1/k\n1FNP1V/buHEjGzduLPpZUZSyf4XnHGqeH3q+yJ4jZ3P0j8bL8wu2/VH9arAwmKqHgYbVZGWhd2GZ\nRWJZu4fekXxZ1fZVbE/so93ZTouzpeYxeWwe5rvnsyO4o+Z7CGYfiqJM6t+filBKFQbN9mb92P5o\nmpzsI5zZD9Fh9aC7+kpahWjC4LXR18pe08ZedfKxrdxKpHVxVrKuAmGwUi23Gqx/Ma+XLBV2ojmP\n1+atuipRMpskp+QqRgw8dgt+s4uwyVR/jkEmjoSEw+KoaCWqtVwplAuDhJzAYrLgczqIpmRyuYIc\nON98Q4SB0+LEb/cLYSA4aFTbH6weGiYMZhtffOKL3PrCrfrPe0IJ0tkcS9sqCIPWHrUsoYEMRAeY\n754/rXO7fF1lCYlL2zz0DkdVn3PHEWwjxYrAsrrHtTywXEQMBEXc8twtnPW7s2q6tlLEIBRPg+xj\nf3IYYvmyjZ62usaoWS76wn1lOQG1WomcFidWk7XISqQJHUUujBjkPxsMyDPodHfitDhFArIAn81X\ndcRAe68XCgPNfuNxWPCb7aowMCBi4LA4MEkm3UpUKcegWisRqFGIonKlchyXxYXHrlp845mCqIHR\nTc5EjoHgIKD1B1u/fn3R8Wr7g02XhpUrnU0Ek0GCySCvj76ul13tzVckWlYYMYgHoe8pOOlaQ5+v\nKAp7o3s5cd6J0zq/y9fFMwPPkM1lMZvM+jjHUzIj4yn8rcvo67Nymq15ijtNzfLAcp7e+zSZbKam\n3R7B7KPJ0cRYaoxMLlP1H3ptJ78wxyAYy2CXmhmOb0cZ34cEhkQMJCQUFF4ffZ2TF5ysv1ZYWrEa\nJElSq7hUjBi4VYEDE4nTI/VH2kySiS5fl4gYCPDavFUXgjiQMHDbLPhNVsZNJrJ2D+aKd5ge8Uxc\nT3B2Wpw4zI7iiEGN5Uq1+5VaiVxWFx67+tkTS8l47Pmljn8h9D1Z669RRKe7UxTemAV87cEtvDlQ\nfW5OPRw+38eN5xwx7fON6A9WDSJiMA00/24wGdRDh5otpyhioPUsMNhGNJYaIyEnpt3ddLF/Melc\numg3QxvnzuEovU4PsiSxIlf///7lTcuRFVksTAQ6rU6170BprfLpoC0WiiIGsTQuc4BUNkVkfI96\n0FO/MFjZvBKTZOLVkeI8g5icXyxVmWMAap5BpYhBLusmGMvnFNjc4D/MsMpES5qWiPknqCnHoFJ0\nTCvx6XVY8GNGkSSilvpq9SfkhP4MSZJodjRXFAZGWYmcFifufMRgvLTJWSoCyfoXgp3uTmElEhxU\nau0PVi0iYjANCv/ovrH/DeZ55rFzOEqb147fWfBBtvWPatv1+e8x9PllPQymoMvXBaidjTUxoZcs\nHYniaVH/eKyMVV/arhStqtGW/VvqqnAkmD20OlRhMJocpcNdXWOkseQYTotTL0MIEIyl8VvbGAf2\nhffgRwJXa11jDKfCLPYtJqfkyhKQa40YgGrnKKwMo0VATDk3wVhq4sS2FYZWJvrTrj/pO6WCuYlR\nVqLCqkR+RV10hE0m6jETafYejWZHc8WqRDVFDKxOwsmJKJ32LK9DXd7EikqW5jfXIgN190HpdHcS\nSUfEvJvhVLNzf6iopz9YLYiIwTTYFd6l1ok2WXhj9A1AXWAXVSRKx6D3MVh1tlo61EAGYqowmG7E\nQBcGBZWJOnx23DYzvSMxtoV24FRg0f7yGu7VssS/hA5XBxv3bKz7XoLZgZbQvj+xf4ozyyltbgYQ\njKdpdqg5BcPRAXA1g7m+PY2x1BhN9ibWtK3h9dHXySk5/bVaG5xBhYhBMoRJMtHk8E9EDEAVBvvf\ngly2wl2qQ0tAFnkGcxuf3Uc6lyaVTU19ch7tve6xTkS+oykZu8WE1WzCn0/cDUv1NbFMZBJFYr+0\n+7EuDGqoSuSyuCpaidw29TMiWlEY1J+A3OFSF2Qiz0DQaGrtD1YrQhhMg11ju1jiX0JPoIcto1tQ\nFCVfqrTARrTzUZCTsPJsw58/ZQ+DElqdrbitbvrD/foxSZJY2u5h53CUbcFtrLD4MI1srXtskiRx\n2qLTeGbgmaIPZ8HcRbMSjSZGq742lAwVNTcD1UrU7lStQ/uSI2rJwTpQFIWx1Bh+u5+j2o4imokW\nlfuMZWI4LU49P6caynIMUmP4bX5a3HZCsYlOr7StUD8vxowR5yAqE811vFYvQFW9DCpaiQo8+b68\ncA1TnzCIy8W76qVWIq1cqcVUveCvZCVyWVx4HJWEQT7qLkqWCmYYU/UHMxIhDKZBb7iXJf4lrG5Z\nzZb9WxgeTxJJysWJx1sfBFcLHPZew5+/N7oXr3XqHgYakiTR5esqihgALGvzsHMkwvbQdlZ4FkJ0\nH8Sq39Ut5fRFp5PMJvnbwN/qvpdg5lNPxGAsNVaUeJzLKYTiaeblcwqGU2Fw11eRKC7HkXMyfruf\nNW1rgOKypTE5VrS7WQ2VIgZNjiYCLhvBeKEwyHccN8BOtMi3CItkEcJgjuO1qcKgGjtRNKPmyhXm\n00RTsr6o9svqgj2spMsvrgJtsa6hCQNFUQVHOpfGYrJgkqpfkjgtzqKqRFqOgSZuosnGNjnbF9tX\n970EgqmYqj+YkQhhMAXj6XGG48MsaVrC6tbVRDNRNu9Wd9r1iIGchh0Pw4oP1W1xqMRAdGDa+QUa\ni32Ly3oZLG33sC8+SCwTY2XrkerB4TfrHt9xncfhsXp4fM/jdd9LMPOxm+14bd6aIwaFiceRZIac\nAq1uN82OZvbJUUMSjwGa7E0s9i3Gb/cXJSCXdoKtBp/NRzQT1a0RoVSIgD1As9tWHDHQKxPVLwys\nJiuLfItEk7M5jiYMSjtvH4hKPTtiKVm34fgzqi0pXGXuQqXnlEYMMrkM4xn1vpls9RXMNCavSpTP\nMUgXCAOLTf38MNJKJCIGgoPEgfqDGYkQBlOg+XaX+peyunU1AM/uVRcResSg70m10oHB1Yg09kb3\nVi0MuvxdDMYGiz4wl7Z5MDvU8morF+XLMw7Xbyeymq2cvOBknnjnCbIGeKYFM59WZ2ttwiC/kNbY\nn19Mt3hstLvaGc6lDWtu5rf7kSSJo1qP4rWRiYhBXcIg3whK27XVrFHNbttEHwMAZxN4Og1NQBYR\ng7lN6XtvOmgVuAoX7ePJiYiBL6X+/ahGbFQiLseLcwwcxd2P07l0TfkFoOYYpLIp/W+PlnzszguD\noqpEoNqJwvULA5vZRoujReQYCGYdQhhMQe9YL6CWBFziX4LT4mR76E1cNjPz/A71pK0PgM0L3e8z\n/PmKojAQnV7X40K6fd0A7I5MtMte1u7GZB9AwsSy+SeAMwD73jBknO9f9H6CyWDFTrKCuUeLo6Vq\nYZDOpollYkU5Btoue8Blo8PRwrCJupubaRVMtCTno9qOonesV19QxeRYTYnHMNH9WPN5a0nOzW4b\noXi6uAtr2wrjSpb6l7BnfI/u1RbMPWqxEsUy6nu90MITS0/kGFjS43gUypoAVkthHwOYsBtqeQbp\nbLquiAGoXZwVRdFFiJpALRVXJQI1AdmoJmeiZKlgFiKEwRTsCu/CZrKxwLMAs8nMquZVDCR3sLTN\no9aPzWVh259g+ZlgdRj+/HAqTFyO12QlguLKRItb3Ficg/gs83FYnbDoROh9HJT6EssATl54MhbJ\nwuO7hZ1IoEYMCssRTodCi4+Gtsve7LbRbvWyz2KuO2IQThcLgzVta/RGZ1Bue6gGv92vP0NRFMaS\nYwQcAQIuGzlFtUbptK2E0R2GzL9ufzdZJcvu8d1TnyyYleiitEorUWl0LJbK6rvtJMP4MdcVMZBz\nMulcGqd1ImJQ2v04k8vUVKoUJoRBQk6QzqXJKTlcVheSJOG2W4qTj0EIA4FgCoQwmIJd4V0s9i/W\nqyWsbl1NnD10t9rVE/Y8C/HRxtmIYmrIs1ZhUJhnYDWbsDqHsMoL1QOrzoHwbhh8pe5x+mw+ju08\nVuQZCIDarEShpNoMTIYgBlQAACAASURBVLMZAHq34IDbRrvJwZjZTMoVqHj9dCm0EgEc2XokEpKe\nZxDLxGq2Emn3jKQiRDNRZEXWIwZAsZ2orQfSUUP8zkuaRGWiuU6tycel7/XxZEGn4GQYn2StK2Kg\n2VlLk4+hQBhkMzVbiTTBkcgk9JwJTSx4KgqD+ZAKQ6r+Pj4drg6GYkN6ErVAMBsQwmAKesd6Wepf\nqv+8vGkVSBkCTflSa1sfBLNdjRg0AK1UabVWIpfVRburvahk6VhyjJw5RDKmVlNgxQaQzOrvYADv\nX/R++iP9YnEioMXZQiwTq6qErdYluDhioO6wN7tsdKCWDx02oIcBTCziPTYPS5uW6sKgtBlTNWi7\ntuF0mLGk+hwtxwAmhA5QUJmofjuRZh0UCchzF7vZjs1kq95KVBIdi6VkPPmuwSTD+Mz2uoRBpYaB\nWoEBLaqYyWVqKlUKEyIgLsf16kTa/PXYLcVViQD8+Y0xgyoTxeW4nkQtEMwGhDA4AAk5wUB0QN+N\nA/CS/96eD9lv+yMsfT/YvQ0ZQ7Vdjwvp9nUXWYm2h9REx2CohUw2pzaK6jrZUGEACDuRQO9lUE3J\n0sKFtEYwlsJpNeO0mWnPqU3Ihk317c6FU2E8Vk+Rp3lN2xpeH1EbndWTfFwYMSgUOpow2B9tTMlS\nl9XFPPc8IcrnOD67ry4rkZzNkchk8djzcyMZxm926Pa7WtAW64XJx1aTFb/db0jycaGVqFSEeOyW\n4qpEMNHLIPxOTc8rZJ5b7S20J7Kn7nsJBO8WZr0w2BHawUO7Hqrp2v5wPwqK3kAIYDzqQ5FdhJU+\niA7D2G7orq9k1K7wLs5/8Hy9q3Ih1fYwKKTLr/Yy0MKc24PqAiQdn8fuYL7u86pzVJ+zAYuTeZ55\nrGpeJbogC3QPcTV2Is1WUCwMMvqiuiOtLqqHlfoSbLXmZoWsaVtDJB2hP9xf1oypGjQ7Rzgd1iMT\nAXuAQKWIgbtV7X1iYGUi0f14buO1easSBqW2uVharezjtpvV3JdUBL/VbbiVCIqbnNVbrhRUAaI9\nSzvmrhQx0Juc1R8xOK7zOKwmK79/6/d130sgeLcw64XBH3v/yA1P36DXFa+G3rBakajQStQ7EiOX\nWsju6HbYt0U92LG6rjG+MPQC24Lb+MyjnymzAtTSw0BjsW8x4+lx/cN3e2g7AVsrStZD77Da2Ebv\n1Lz1gZrHX8j7F72fV0deralUpWD2UFPEIDWGhFQkgkPxNAG3umBoT6qlFYerTGqu9JxCuxKgNzp7\nbug5NXmxRiuR1WTFbXUTSUWKhE6zS8sxKPkcal1hmDDo9nfTF+4jp+QMuZ9g5uG1eau2EhUKA82P\n73VY1PwXJYff5iWSitTso69kJQJVGGhWonrLlUI+YlBqJXJUyDHwGicMWpwtfHjJh3mg94G6KzcJ\nBO8WZr0w6GnuIZPLFHntp8uusV2YJbOeyAvQOxLFQze7wr0ktKTdjiPqGmNfuA+H2YFZMnP1I1cz\nGB3UX6ulh4FGl68LmEhA3hbcxsoW1b6wcyQvDHzzYOHxxtmJDns/CgpPvvOkIfcTzEw0YVCNQAwl\nQ/jsviKvcTCWJpBfVHvjQZxK/Q2FwslwmTDo8nfhtXl5ZuAZgJqtRKDmGUTSkSJrlNNmxmE1FUcM\nYKJkqQHJi0ualpDMJnX7oWDuUZMwsBQ3NwN1p52kGnnw2/3IilzUXbgaShfrGqURAyOqEpVZiWwV\nhIHFplY2i9RvJQK49PBLSWaT/GbHbwy5n0BwqJn1wmBFYAUw4a+vhl3hXSzyLsJqnghx9g7HWORe\nQVbJsm3oBfUDxt1a1xj7In10+7v54Zk/JJ6Jc/UjV+vt4mvpYaChCYP+SD/pbJpdY7tY3bqKDp+d\n3uHYxImrzoHBVyH0duUbVcGKwArmu+eLPIM5TsARQEKqqmRpaXMzUCMGLXkbjhQbpR0Lw/HhusY2\nlhrTm0FpmCQTR7UexXNDzwHlu5vV4Lf79RwDq8mqL4ha3PbiqkSg5hkkxyA2UvPzNI5pPwaA3+74\nbd33EsxMfDZfXREDrRmYx26BfL8Pf35O1rojXinHAEqEQa5+K9FkEYNYqkLTTd98w0qW9gR6OGHe\nCfxy2y9rciYIBO82Zr0w6PJ3YTVZ2RHcUfW1u8K7WNo0YSOSszn6RmMc0aJGCN4Y21l3tADUXIZu\nfzcrmlfwn2f8J0OxIT7z6GfYG91LXI7rCU7VMt8zH6vJSn+4n96xXmRFZkXzCpa2eejVIgYAq/J2\nom1/rPt3kSSJ0xadxjODz+i7N4K5h8VkIeAIVBUx0Gr+FxKMpnV/PrFh2s3OuoVBOFUeMQC10Vk0\no86Lwl3UavHZfHqOQcAeUPudAAG3tYIw6FG/GlCZaGnTUs5ecjY/3/pzUVt9jlKNMMjkMqRz6SIR\nrEUMPHYL5Jv0+fLNyGoVBolMPsegRGy3OFoIp8LqOLLpog24aigsV1opxyCWlosbC4JamcggYQBw\n2eGXMRwf5i/9fzHsngKBxje+8Q2OO+44fD4fbW1tnHPOObzxhjHNaSsx64WB1WRladPSqiMGmWyG\n3ZHdRYnH74QSpLM5Vncuot3VzuvpYN3CICmrof8ufxcAx3Qcw62n3cqO4A4+/cingepLlWqYTWYO\n8x5Gf6SfbUF14bEikBcGw9EJz2jzEug40lA7USqb4pnBZwy5n2Bm0uKsrvtxKBUqWrCn5RzjKVn3\n5xMdod3qrUsYyDmZ8cx4RWGg5RlA/RGDcCpMKBnSyzKC2r25YsQADMsz+D/v+T8oisIdL99hyP0E\nMwst+Xg6+QDaxo3H6tGPabYbj6MgYuDqAKi5MtGBrESgbggYFjEosRJ57RYUBeKZkqiBbz6E6+8f\nonHygpPp8nVxz5v3iJ4GAsPZuHEjn/3sZ9m8eTN//etfsVgsfOADHyAYDDbkebNeGIAa6tMq8kyX\ntyNvk1WyRaVKd+YTdpe1e1jt7WKLzQzth9c1trcjb6Og0O3v1o+duvBU/u3kf9O7mNaaYwBqAnJ/\npJ/toe04LU4WeRexrN3DeEpmZDw1ceKqc2D332B8X83P0ljbsRavzSvsRHOcVkdrVcnHoWSoqLnZ\nWEFzMzIJSI/T4WhmODFcc4KtVrGltCoRqM0LNeoRBnqOQT5ioNHstpXnGHjngd1nmDCY75nPxYdf\nzIO9D7J1/1ZD7imYOXhtXrJKdlr9Q2IZ1U5aKfnYbSsQBh6103jNEQO5csSg2TnR5Kye5GOryYrF\nZCnqY1AYMYCJSIiOgU3OQLUiXrLqErbs38LLwy8bck+BQOPhhx/myiuvZPXq1Rx55JHcc889jIyM\n8PTTTzfkeXNCGKwIrGB/cn9Vu5daPfDiikSqMFja5mG1xctuq5Vwc1ddY+uLqOUFtQZFGmcvOZsb\nTriBxb7FRcnP1dLl72LP+B62jG6hJ9CD2WRmaZu6Q6QJHSDfuVmB7X+q+VkaVpOVUxacwpPvPEk2\nV8HfKZgTVNP9WFGUsohBML+IbnHb1NLAQLurAzkn697katFKiFaKGPjtfj1CWJeVyO6rGDFodleI\nGEgStPYYYiXS+NSRn8Jv93Pri7eK3cs5hlbRazolSzXbXOGCXSvt6S2MGOQ3pmrOMcjEMUmmsuRi\nraTx/uT+usqVgioEErJqJbKb7XoBA49D/TpeVrJUa3I2iFGcs/QcfDYf97x5j2H3FAgqMT4+Ti6X\nIxAITH1yDdTXQnSGsKJZTUDeEdqhV0uZit5wLxKSbvEBVRi0ee34nVZW5+s9b5EyrKtjbH3hPiQk\nDvMdVvbaBSsv4IKVF9RxdzUBWc7JvDb6Guf3nA+oEQ9Qf591y/7/9u48Pur6Tvz46ztXZjJHTnJx\nBhIggEo5RLQFLYqiQrvV1l3vanVdL5DV/rTdLrRrPdZt165HXaqCtkVs1ardWhXlFloRueRQkYRw\n5YKck8lkju/vj+/MkElmJpNkcs776YOGzHznO998O5/wfX8/7/f7EzgfOSWQOU5LJ5pxS4/eE+Cb\no77JO6Xv8MrBV7h+0vU93p8YfLIt2ZxqOYWqqqE8+2icHidev7fdGgZtZgyc2rR/rn0EnISq5qq4\nx3JbwYubSIEBaOlEh+sP96grUZopDY/fQ4Wzgln5s0KPZ6aaaGzx4vH5Merb3JMZNhG+TFxussPk\n4I5z7uCxjx9jy/EtfGPENxK2bzGwBdfRaGxtJM+aF3PbYNpN2DoGYV2JAoGBXUtl7cr6CG25vC5S\nDakdfgcEZwd7OmMAWpqSy+vCr/rDipyDKzhHnDEArTNRsM6nh1KNqXx3/HdZuW8lxxqPMcI+IiH7\nFb3srw9Cxd6+fc+8s2DBY91++eLFi5k6dSqzZ89O4EGdkTQzBkCXCpAP1x2mwFYQ9kvmUFUT44Zp\nv0Qn12tdRPbVfdmjYyurL+vwPokUDGz8qj8UIOU6UrClGMJnDBRFmzUo3QSu2h6/77xR87ho5EU8\nvv1x3jr0Vo/3JwafLEsWbp87dGcyltoW7TMXKTDIbDtjkKbNnnW3ziDYQjRaYPDNUd8kz5rXoQi6\nK4Idj1p8LWGpUaFFzjrUGUwAZxU0Jy5f9Hvjv8co+yh+ueOXeP3ezl8ghoRgYBDzIt7TAr//Hs7t\nK4COqUQpBp0WuLobQJ9CijkNk87U7cCg2dsccV2QUCqR63SP2pVC+IxB2/cKruDcoWVpAhc5a+uf\nJv4TOnT8/sDvE7pfIYKWLl3Kli1beP3119Hr9b3yHkkxY5BuTicnNadLBcjtOxKpqspX1U4WnqN1\nCHJUHWB0RkrE1Yq7orS+NNRWtDe03ffEDK3QUVEUxg2z8lW1M3zjkkXw0ZPwxXtwzj/26H0NOgNP\nzH2Cuz+8m3/f+u+kGlO5ZPQlPdqnGFzarmUQvGCJptatBQZtL9iDF9AZqSY4FggMMouAHgQGgVSi\nSDUGABeOvJALR17YrX0HpZnO7LvtzxNcwfl0cys5DvOZFwQLkGu+gFHn9ei9g4x6I0umL2HphqW8\ndegtrhp/VUL2Kwa2YCpR1M5Efj+8eQd8+R7OEVPA2DEwsAXy8mmpB7O2P5vJRlNr5wF+JM2eyCuJ\n2412DDqDlkrk94StX9JVwcDA5/eFvZc1MGMQNTA4sg2mXqfdGEuAXGsu88fM50+H/sRdU+/CZrJ1\n/iLRv3pw576v3XfffaxZs4b169czduzYzl/QTUkxYwDarEG8gYHP76OsviysI1FNUyv1Lo+Wn+9u\ngtoyJqfm9ygwUFWVsoaysMLjREtPScdhcqBTdBRlFIUeHzfMFj5jAFDwNXAMT1h3ohR9Cr+66Fec\nnX02P9z0Q7Yc35KQ/YrBISvQ5jBmnUHzaXjtVmo/XQkQVqwbXCU4PdUYmjHIzhyPTtFR2dy9IvnO\nUokSoe0aCW1nHjJCqx/3XsvSti4edTFTh03lmV3PSOvgJNE2lSiitT+BfX8C6zCcgTqdDoGBORgY\nNIA5LbTfbgcG3uaIM+KKopBpzqTGVYNP9fUolSjajIE9OGPQvsbAkAIzb4Ndv4P3/y0hCwwG3Tjp\nRpweJ3869KeE7XOoa2ht4N5197Jiz4r+PpQBa/HixaxevZp169YxceLEXn2vXgsMnn32WQoLCzGb\nzUyfPp3NmzfH3H7jxo1Mnz4ds9nM2LFjee655xJ6PBMyJ1BaV0qrr7XTbY83HafV3xoWGLQtPKZK\n6/YxJWsKVa6qbt+9rGyuxOV19eqMgaIoFKYVMsYxJuyX87gcGxUNLeF3UnQ6mHglHPoAWp0R9tZ1\nqcZUnrn4GYrSi7hv/X18UvFJQvYrBr5sszZjELUz0cndsGIufPYatWXaStltL6Rrm1tJsxi1tIam\nKjCnYTBZSU9J71HxsUEx9KiGoDPRZgyybMFUonaLIKWNgtQsWP8ofLk2YcehKAr/OuNfqXZV89L+\nlxK232TwaeWnoQYUg0nM4uO/PQfbnoZz/xmm3YSzteOaHU63V+tIBIEZg0BgYLTT4OlmKpEncmAA\nWgFypVML8ntUfGy04PK4OgQhwRkDZ2uEdLoF/6mdi21Pw1+WarMpCTA5ezLTcqbxu/2/o6y+LCH7\nHMqqm6u5+d2bWX90PX/4/A/SMCGCu+66i5UrV/LKK6+QkZFBRUUFFRUVNDV1L1jvTK8EBq+++iqL\nFy/mRz/6ETt37uT8889nwYIFlJeXR9y+tLSUyy+/nPPPP5+dO3fy0EMPcc899/D6668n7JjGZ4zH\nq3pj/7KvPwabnuCrz9YAhLUqDQYGRTk2qNoHwJSRXwfo9qxBaX2gI1EvzhgAPHjug/z0/J+GPRbs\nTHS4ut0Hq2QheFtgzx8SdhfFYXLwv5f8L/m2fO5edzf7avYlZL9iYGubStTBrtXwwnzw+2D8ZdQF\ntmlfY5DZZnEzbFo/9UxzJqdd3Q8MHCmOTouhe6LTGYP2LUt1OrjhT2DJgN9fDW/fm7A2ilNzpnLJ\n6Et4Ye8LPP7x43xR2/WFHpNJdXM192+8n5vevYl/3fCvg+4iJZi60mHGYP/b8O6D2o2fyx4FRwHO\nwL/+7Vc+Ds0YuBu0Vrr0LJXI5XVFbf+bac6kollbjK+nxcfN3mYtCDG2DQyidCUCbdwteBwuWAKf\nvAhv3QW+xNTj3Dn1Tk61nOJbb32LBzY+0OV26cniaMNRbvjrDRxrPMaCwgVUNldyrOlYfx/WgPPs\ns8/S2NjIvHnzyM/PD/35r//6r155v14JDH75y19y8803c9ttt1FSUsJTTz1Ffn4+v/71ryNu/9xz\nz1FQUMBTTz1FSUkJt912GzfddFNCf+hQAXL7fxj9Pi2nfvU/wpNnwbqH+WrXKoCwGYNDVU2kmvTk\np5mhcj+YbEwcdSF6Rc++U9270C1rKAN6PzCYkj2FqTlTwx4rytH+MeiQTjRqtrbg2f8tgadnwMYn\noPZIj48h05zJiktWkJ6Szq3v38rSDUv5/YHfc/D0QWlpGsXxpuO8vO9lbnnvFp7Y/kR/H06XOVIc\noRziEG8r/N9SePNfYMRMuH0jTPoWpxUw6gxhaQCnna1kpAbuIjZVg1Xrp55lzgrfZxdEW/U4kaLN\nGKQHfpbTTRFmLfPPgds3wPn3wqcvw68vgLLE9Kh+6NyHmDtiLms+X8NVb1/FP/3fP/HHL/7Y7Qu9\nociv+nn14KssenMR68vXMzt/NofqDnHg9OBaC8KoM2IxWMJnDMr/Dm/cBiNmwFXPg06vBQaKDqNi\nCFtx2NnavsbgTCpRvCsqtxet+Bi0fxcSMmMQSCVq/15aIbXSsStRkKLAxcvhoh/D7tXwxg/A54m8\nbRfMyp/Fu1e9y82Tb2bz8c1c/eeruefDe9hTvafH+x4qDp4+yA1/vQGnx8kL81/g9rNuB5CsgghU\nVY34Z/ny5b3yfgkvPm5tbWXHjh3cf//9YY/Pnz+frVu3RnzNtm3bmD9/fthjl156KS+99BIejwej\nsfu/MI4e2kvdicP4VB9GxcBHe96h8LiKgoq9Zie5h/6AufkEreZsKif9Mz5DKqXHV5JhGM7uI25A\nWwRsZ3kd44bZtDuNlfsgpwSLycooxyi+rO1eZ6LS+lKsRmu32i721OgsKwadwpYva8ixm8Oe0897\ng+zyv5JT+iZp6x+G9Q9Tn3MuVYXfosU6skfv+0D6Nbxet46dx7ez9oiWNmFRUhhvHk1hSgEWJQWT\nYsCkM2JStD8GRY+CgnaPV/vam3d8e4NfVQGV4P/q0GHWmTArJsy6lNDfK72n+cS5n+3NBzjSqvXY\nztQ72F6xHWuVk2/Yvxa2X/uw4YwpmdH3P1AMR7/cTd3JMgAcSipfln7K3qa3UFQvo/Y+haNmJ8dK\nbqNs6v1wUsHmyqVOr8OuWPjo0JkL/uN1rlAXMJxVWos3tG4m3Z2lq2/t/cDAarSiV/T4VF/Yexn1\nOhxmA/tP1rPlyyh1F4WLcVgvoHjbA5hXXcGJid/ndMGFPT6mm3Vz+M6I6XzUtJsNDTv42baf8fjf\nHuVsSzEOvY1UXQpWnZlUnYVUnZkUnUkbZ2H/DZ5x51dVgv/5VT9+VAyKnnS9nXS9DYde+/8I4Ij7\nJC+ceotD7mNMNo/lltxF2HWpbOdjVm56khuzrgjbtyNnJKMnTuuPHyuqI5/voqFSu4FjUY2Ul+9j\nr+st9N5miv/+EF5LHrtnPYu3zAk4sdal0qxTMCvGsM/iqaZWCrMDBbNtio97VGMQpfgYtMCgxdcC\n9GzGIBgYGHSGsFQiRVGwphj4sqop+pgDKLiF4dP8FH76KKfqGjgx4aZuH0tbFzOW8/KX8H7DNt49\nsY0NxzZQaCog25COTZ+KXZeKXW/FrkvFoktBh4KiaKNNFxx3g2bMaePMp/rx48ev+jHpjOQYMskx\nZGBqE/gdcJXyX5W/w6JL4cd5N8OBwzSrKnZdKmv3vEHRyfB71o7c0YyeMBXRNxIeGNTU1ODz+cjN\nzQ17PDc3lw8++CDiayoqKrj44os7bO/1eqmpqSE/Pz/suRUrVrBihVakUl1dHfN4jn/wa86r0FqH\njS/I5VTzh5y1+5XQ85t8Z7Ha9z0+aJmGd4eBdBqZUGgitcHP9S/8PWxf18wYqaXXVO3TOvgAxenF\n7D+1P+YxRFNaX0qho7BfBr5Rr6M4184bO4/zxs5IS8OPBhYzQqnmW7qP+E7FZoqrfpyQ954X+HpS\nr2eHOYVPzSl86m7kTZOkOQAoqspUt5vvOl18s9lFvrecH+TlsKrqj1y+8ynGeM/c/dqevoAxJWt6\n/Zi6NObWPsN5Va8CkFeQi6+xkrP2vglAk2rmXzyL+evOWbBzBwB2mrlwlA7V6esw5uYUB4LmdjMG\nPakxGGHr3f7iiqLgMDlo8bVgNoQH3cMzUnlvXyXv7YtdPJ3Kch4yrOaGgy8y/OCLCTu2C4AHgM9M\nJt6wW9neupuvdDoadDq8g+QCJBEUVSXD7yfL5+Ow0Uia38+jp2q5wlmOwgYALsrJ5mPfFh7Z/Spt\nb019nLmQ0RN/1+vH2JUxV7H2V8yqeQOAzOF5GBoqQmOuRnXwnYbFlP/+zA2sLOqZP1KHr0XtMOZy\n7CnaX9oUH9uMNho93Z8xiFZjEGxZCj2bMQiuY6BX9B2CkFy7mbX7K1m7v7OGBWdxvf77PHx8JVnH\nP+z2sUQyG3hAUfiD3cam1BZq9TpKdXrq9Mkx7hRVJcfnY5THS77Xy3vWVAq8PlZUHCbv0JmbyOfl\nZLPP3cBZe98Oe/3fs77N6AlSJ9VXeq1dafuL3c4WOYq0faTHAW6//XZuv12bdpoxI/bd0lGX3suB\nqm8BkHvyD2xv2sf+y55CURRaU/Ox2EdwK3BrYHu/6ueejY+w0N3Mf9wRvnjEpHwHNJ7U+vznTgGg\nKKOI94+8H/OuSDRlDWXMyO2/u70v3TKTI6fi6VayiNOqiqvuc/TdnE6OZlzgz3fRzn2r6qHV76VV\nbaXV78GtevCqXrRPg4qqBu+7Dw4q6pk7rgoEZzx8qh+32kqLv5UWvxuX302L341db2W6rYR0g3an\nrgn4EviBp44flv2Se4pm8PPR92IMtPbLy4y9iFGidGXMjbzsPg5Ua+0xzUdf4Li3gQPTngHAbR/N\nLak5tF9C78m1ZgpNBn7RbsxNLnBofdfd9WAbBmh3GZ0eJy3ejhfenalvqWdK1pQuvaY70lLSSPV3\n/H0Q/5gDuIi9dV9hcCdufYMgA/C9wB/Qft96VC9Ovwunz4Xb3xoaZ/7APJd/kOTbB2fkdME7r4oO\nHQqtqpc6byN13gbtq6+ROm8j840ZfDd7PjZ9Km37Qn2tcR9rj69kzdeXMcM+OfR4flZBn/wcXRlz\nIy6/nwPVWotpw5FnqFB0HJj+LwC0pI3jF23W0wBA9fPyu8vIMxt5us2YU4DJBWlayp/XBYG2vjaT\nDZfXhcff9RWK23cKaqvtOh9tU5q6ymKw4Pa5UVA6vNdvbz2XI6fjHXOz2VN/PcZupip2ZlbgT5Cq\nqjT7W2j0OXH53docV2C2y9/m74OBTlEC406HPvC1xe+msvUUFZ4aKlpPUek5xRetNRSl5HJfwY3U\nnm2l7apJI05vYW3Vm2yc9xw5pjOfjeFZw/v+B0piCQ8MsrOz0ev1VFRUhD1eVVXVYRYhKC8vL+L2\nBoOBrKysHh1PQeFECgq11k7nHqhh3ccfk332NHJScyJuf7LpJC5FZUJTNTMddVq+fVvlgdmB3EkA\njE/XWg0erj/MlOz4LziaPc1UOCt6vb4glhy7uUMaUWw9WeNZ9NSjo/O4e93d/EW3h4dmPdTfhxPV\n8LElDB9bAsAY31aOHttMyaxLY76m3mRikt/NzDGZHZ+s01KqQjMGgTaop1tOU2CL/yJNVVXq3HW9\nnkoEWsG9T+1YO9P1MRfhfIg+UeT/Jr/5w5vsNBzjhllL+/twYho+djLDx2rBS27Tn6lsrux0zD1n\nNJMGkcecM3C5FpgxCHY7crY6STfHP348Pg9evzdmKlFQTxc4Ay0obP9eOQ5z+LohnZIx11/0tYWs\nfPtN6vJTmVsU+/Mrek/Ci49NJhPTp09n7drwtntr167l/PMjX1jOnj27Q5rR2rVrmTFjRo/qC9oL\nFiDH6hDwVf1XAIz1eODgOx03CHQkIkcLDIJrA3S1zuBIg5YP2p+BgRhc5o6cy/Ul17P64GrWla/r\n78OJSzDtx6/GbgVYq0B6c0PkTljOQDtgmxYYBC8muppO5PK6aPW3Rl3cLJGuLbmW60qu6/X3Eb3H\nqDNy+djL2XB0Q2j9i8Eg3kJhp8FIarRC25bAzxtc4MwY6HbUxXSiZq92pz7ajEEwyIeeFx9H+rsY\nXIrSi0hLSeOTSilA7k+90pVo6dKlrFq1iueff54DBw6wePFiTpw4wR133AHAjTfeyI033hja/o47\n7uDYsWMsWbKEAwcO8Pzzz7Nq1aoOBcw9NT5Tu7sfa6Gzw3VaO9NxjrHweYTAoHIf2AsgVbs4GWEb\ngVlv5su6rgUGwDEpKQAAHTpJREFUwValvbmGgRh67pt+H5OyJvGTj35ChbOi8xf0s2xLNj7VF1px\nOBKP30OD6iXD4wotZBamKZBfbQ0PDKKujxBFXyxuFnTF2CtYOG5hr7+P6F2Lxi3C4/fwXtl7/X0o\ncXOYHJHXMWjHqdNj87gjPxkKDM6kEkGMhdOiCC6sF2sdg6AeFR+3aVEaLQgRA59O0TE9ZzrbK7b3\n96EktV4JDK655hqefPJJHn74YaZOncqWLVt45513GD16NADl5eVhaxoUFhbyzjvvsGnTJqZOncrP\nf/5z/ud//oerrroqocflMDnIt+bH7OV9uP4wGSkZZEy8Esq3gbPdxUfl/lAaEYBep2ds+lgO1R7q\n0rGUNpSiU3SMcozq0utEcjPpTTwx5wm8fi8/3PRDvP7E9N3uLfGsfhy8YM/w+aEmQtDeFCgaDNQY\ntE0l6opgcNIXgYEYGkoySyhKL+Ltr97ufOMBIthBqLNZOqeiYm1tjjxL1y4wCKYSdbUzkcvrAoia\nStR2nY+ediUK6mqtnxhYZubN5HjTcU42nezvQ0lavbby8Z133klZWRlut5sdO3YwZ86c0HMbNmxg\nw4YNYdvPnTuXTz/9FLfbTWlpaWh2IdEmZEzgi9ORAwOv38v2iu0UZxTDxCtA9cMX757ZwOeB6oOQ\nOznsdUXpRV2eMSirL6PAWkCKPqXLP4NIbqMco/j32f/Ozqqd/Hp35LVBBoqYi5wF1LUELtj9fqiJ\nMDaDqUSBGYOMFO1ioqtrGQQDg75IJRJDg6IoLBy3kN3Vu0PpnwOd3WRHRaXJE/si3qn6tVSilgiz\necHAIKV3U4lS9CmhfScqlUhmDAa3GXlaob2kE/WfXgsMBqrxmeMpayjD7es4hfr2V29T3ljOtSXX\nQv5UcAwPTyc6dQj8HsgJDwyK04upcdVQ21JLvErrS6W+QHTbFWOv4LqS6wb8ZygYGMRK+6l1a+Mm\nQzFBTYQAu6lau0AxagWEqcZULAZLt1OJJDAQXXHl2CvRKTr+/NWf+/tQ4hK8ux8r7cev+mlWPVj9\nKjSc6LiBO5CKlKBUolh38YOpgT1tVxokNQaD2/iM8ThMDgkM+lHSBQYTMibgU30cqgtP/WnxtvDs\nrmc5O/tsvjnym9qKiBMWwKEPoTXQ6qwyUHjcbsagOKMYoMM+o/Grfo40HBnwF3ViYHvw3Ae5cuyV\n/X0YMcUzYxAMqDPSRkJ1hFQiZ1Wo8DioO2sZSCqR6I6c1BzOyz+PP3/1507TcwaCeAKDYIqPVfVD\nQ4SUjXbFx91NJQrOGMS6WA8FBj1sVxokqUSDm07RMS13mqyA3I+SLzDI1DoTtU8nevXzV6lsrmTJ\n9CVn1k6YcLnWy/nwBu37yn2gM0D2+LDXFqV3rTNRhbOCFl8LY9LGdPvnEGIwSDV0fnc/eMGekVEU\nfcbAGh4YZFoyuxwY9GXxsRhaFo5byAnnCXZU7ujvQ+mU3WQHYgcGTo8TQJsxaIwwY9DSACgQ2JfV\nqK1A3tVUolCNQYz0nmBgkIh2pZ29lxgcZuTOoLyxnEpnZ4vSJYdNmzaxaNEihg8fjqIorFq1Kux5\nVVVZvnw5BQUFWCwWLrzwQvbt29ft90u6wGCkfSQWgyWsM1FjayO/2fsbLii4gJl5M89sPOYbWgrD\n53/Rvq/aD1nFYAj/BZaTmoPD5Ih7xiDYkajQITMGYmhTFIUscxY1LdFnDIIX+OnDSqDhGLjb3ZV0\nVoUKj4OyzFndqjFINaT26M6kSE7zRs0j1ZA6KNKJgoFBrM5EwfoDq98fOZWopV77t0+nXSIYdAYs\nBkvvpBJZep5KJDMGQ0vwOkzSiTRNTU1MmTKFX/3qV1gsHWff/vM//5Nf/OIXPPXUU2zfvp2cnBwu\nueQSGhu7tyBt0gUGOkVHcUZxWGeilZ+tpN5dz+Jpi8M3Npig+BL4/F3w+7QZg3ZpRKBd/BSlF8U9\nY1DWUAYgMwYiKWRZsmIXH7vrsBvtGIdpi6Jxqt04aqrqOGNgzuS0q+szBjJbILrDYrAwf8x83j/y\nfugu+EAVCgzc0QOD4AW71WSPXmNgDq/FCXY76oqupBIlql2p1BgMfhMyJmA32qVtacDll1/OI488\nwtVXX41OF37ZrqoqTz75JA8++CBXXXUVU6ZM4aWXXqKxsZHVq1d36/2SLjAArbjl89Ofo6oqNa4a\nfnfgdywYs4CSrJKOG0+4HJpr4Kt1UH80rFVpW8UZxRyqO4QaqfVbO6X1pdhN9rAezkIMVdmW7NjF\nxy212mqqwRS9tulE3lata4qtY2BQ667tUs53nbtOCo9Fty0atwinxzngFxfsUiqRJTP6jEGgviC0\nX6O9005H7YVmDGKk95wz7BzGpY0LdSfqjrbBgFnflVWOxUCk1+mZljttUKTu9bfS0lIqKiqYP39+\n6DGLxcKcOXPYunVrt/ZpSNTBDSYTMibw2hevUdlcyQt7X8Dj83D31+6OvHHxJaAzwqYntO9zp0Te\nLL2YJk8Tlc2V5FnzYr5/sCNRqJZBiCEs25Id8xd8bUut1oI0cywo+vACZGdwcbN2qUSWLPyqnzp3\nXeiOY2dkxkD0xPTc6RRYC/jo+EdcMfaK/j6cqOwmOwpKzHqAYGCQas2NUnzcccbAZrLFtXBaWy6v\nC4POEDN9b86IOcwZMSfq8/Ew6oza++iM6HX6Hu1LDAwzcmew8dhGqpurGZY6rPMXdNPjHz/OwdMH\ne23/kUzMnMj/O/f/JWRfFRXaQqe5ublhj+fm5nL8+PFu7TMpZwyCBcgfln/Ia1+8xneKvxN9oTFz\nGhR+A47+Xfs+J/KMQVGGVoAca/G0oLL6MlnxWCSNLEsWde46PH5Ph+f8qp9DdYcYbhuupe5lFoav\nZRBcwyBCVyKgS+lEde46CQxEt+kUHS8teImHv/5wfx9KTDpFh81oi2vGwGbLizFjkJhUor4qBg42\nOhBDg6xn0DXtbzSrqtrtm89JOWMwPkNLWXhyx5MYdAb++Zx/jv2CCZdrqUQpaZA2IuImwc5Eh+oO\nxbz70dTaRJWrSlqViqQRbFl62nWaXGv4XY0Dpw9Q7armGyO+Edh4fHgqUVNwxqBjKhF0bfVjSSUS\nPdXZbPBAYTfZY9YYhFKJ7MPBdRo8LmiTp68VH4fX09mNdo42Hu3ScTR7mvusGNhisGDQJeUlzZA0\nMXMiVqOVTyo+YUHhgl57n0Tdue8veXna76SKigpGjhwZeryqqqrDLEK8knLGwGq0MsI2ghZfC9dP\nup6c1JzYL5hwufY1d5K2vkEEaSlp5KTmcKg2dmeiYOGxdCQSySJ4dz9SZ6JNRzehoHDB8Au0B7LH\nawsJ+rza902BdnXtuxJZtH3G25nI5/fR2Nqo1TIIMcTZTfa4ZgxS0wIXEo3t0oncHWcMbKbYsxCR\nNHub++wuvsVgkY5EQ4hBZ+BrOV9je6UUIMdSWFhIXl4ea9euDT3W0tLC5s2bOf/887u1z6QMDAAm\nZ0/GYXLw/Snf73zjtOEw9TqYclXMzYrTi/myLnZnolCrUpkxEEki1urHG49t5OxhZ5+pE8ger60u\nXndE+z6YStTDGYOG1gZUVEklEknBkeKIWQ/g9DjRKTosaYEU2rZ1Bn5/oMagXfFxINiIp8FGUF+m\nElkMFlnDYIiZmTeT0vrSmF3tkkFTUxO7du1i165d+P1+ysvL2bVrF+Xl5SiKwpIlS3jsscd44403\n+Oyzz7j55pux2Wxce+213Xq/pJ13e/DcB3F6nKEVHTv17Wc73aQ4o5jtB7bj9XujTmmW1peiV/SM\ntI+M+LwQQ0201Y+rm6vZd2of937t3jYbBzsTfQFZ47RUIpMNTOH/4KelpKFX9DG7HbUVXNws7vEu\nxCBmN9o52hQ97Sd4wa4EU2Pb1hm0NgFqxBoDj9+D2+fGbIiv84/L4+qzu/iTsyf3aC0EMfDMyD1T\nZ3DZmMv6+Wj6zyeffMJFF10U+n7ZsmUsW7aMm266iVWrVvHDH/4Ql8vFXXfdRW1tLbNmzeL999/H\nbrd36/2SNjDItmSHLlgSpSi9iFZ/K0cbj0adEShrKGOEfYQssiSSRijtp91F/ObjmwHCa3Kyi7Wv\n1Z/DhAWBxc06pvrpFB0Z5oy4ZwyCqyvLjIFIBvGkElmNVrDnaw+0Xf24RQuiSQkPooPtRJs8TfEH\nBl5X56m6CbJs9rI+eR/Rd0qySrAYLHxSkdyBwYUXXhhzpk5RFJYvX87y5csT8n5Jm0rUG4KdiWIt\ndFZaXyr1BSKppOhTsJvsHWYMNh3bRJ41L9QMAABLOthyzxQgR1jcLCjTnBl3jUFwxkACA5EM4ik+\nthqtWrqQyRaeShR8XYQZA4i9PkJ7fZlKJIYeo87If1zwH3xvwvf6+1CSigQGCTQubRwKCofqIhcg\n+/w+yhvKpb5AJJ0sc/jqx62+Vrae2MrcEXM7tlTLHg81gbUMnNUdCo+DMs2ZMmMgRASOFAfN3ma8\nfm/E50OBAYCjABra9DsPzhgkIjDwNIetSixEV1065tLwm0ei10lgkEBmg5lRjlFRZwyONByh1d/K\nmLQxfXtgQvSzbEt2WGDwScUnuLyuyK19s8drNQaqGnPGIMuSFXeNQTAwSDNLu1Ix9AVraaKtO+D0\nOM/k/tvzw7sShQKDKKlEXVjLwOV1yYyBEIOMBAYJVpxeHHXG4OldT2PWm5mdP7uPj0qI/pVtyQ5L\n+9l4bCNmvZlz886NsPF47eKk4YTWYz1CjQF0bcag3l2PXtFjN3avGEuIwSTW3X1VVSlrKNMWFYTA\njEHbwCCYShQ+uxbaZ4wVldu/T1+2KxVCJIYEBglWlFFEeWM5Ld6WsMc/Ov4Ra4+s5bazbyPflt9P\nRydE/2g7Y6CqKhuPbWRW/qzIRYzDAtPG5du0r9bIqURZ5ixcXhfNnuZO3z+4uFl3V4IUYjAJBsCR\nWpaWN5ZT767nnGHnaA84CrQZA79P+z5K8XFXU4ncPjd+1S9rCwgxyEhgkGBF6UX4VT+H6w+HHnP7\n3Dzy90cY4xjDzZNv7r+DE6KfZFmycHqcuLwuDtcf5njT8egrhAdblpZpXYtizRhAfGsZyKrHIpkE\nL+IjBQZ7qvcAcHb22YGN80H1afU8oC1uBj1OJWr2agG7zBiIgaQr63AMZbHOgwQGCVacobVbbJtO\n9OJnL1LeWM6PZv0Ik97UX4cmRL8Jrn58ynWKTcc2AUQPDBzDwWiFsi3a9zFqDCC+wKDeXS+FxyJp\nOAJ3+yPd3d9dvRur0XqmCYYjkFIUXMugpR4MZjCkhL0u1ZiKTtHFnUrk8rq010mNgRggjEYjLper\nvw9jQHC5XBiNkdvmS2CQYKPsozDpTByq1QKDow1HeX7P81w65lJmF0htgUhObRc523hsIxMzJ5Jn\nzYu8saJo6xmcCgTXUboSBYMNmTEQIlyw+DhSYLCneg9Tsqeg1+kDGwdSW0OBQUOHjkSgrR1iNVrj\nTiUKpvhJKpEYKHJycjh+/DjNzc1JO3OgqirNzc0cP36cnJzIN92SdoGz3mLQGRibPpYv6r5AVVUe\n/fhRDDoDD8x4oL8PTYh+EwwMDtcfZlfVLm4969ZOXjAeTu7S/h5jHQPouHBaJPXuekoyS+I/YCEG\nsWj1AC6viy9qv+CWKbe02bhA+xrsTNRS36G+ILSp0d7lVCKZMRADhcOhfa5PnDiBx+Pp56PpP0aj\nkdzc3ND5aE8Cg15QlF7E9ortrDu6js3HN3P/jPvJteb292EJ0W+CgcFbh97Cp/qipxGFXhCoMzCm\nQoot4iaZlvhrDCSVSCSTVEMqekXfocZg/6n9+FTfmcJj0Ir7dYYzMwbuyDMGEFhROc5UouCMgdQY\niIHE4XBEvSAWGkkl6gVF6UVUNlfyyN8eoSi9iGtLru3vQxKiX2WYM1BQ+LTqUzLNmUzJmhL7BcHO\nRFEKj0FbUdlmtHUaGLR4W2jxtZBulsBAJAdFUbTVj9sFBsHC47OGnXXmQZ1OK0BuW2MQJTCwmWxx\npxKFagwklUiIQUUCg14QLECuclXxk/N+glEXucBDiGRh0BnIMGcA8PXhXz+T3xxNcMYgShpRUKY5\ns9NUotDiZlJjIJKI3WTvcBG/p3oPI+0jQ2l4ZzbOh8a2gYGkEgmRrCQw6AXB5bsXjVvEtNxp/Xw0\nQgwMwS5Cc0fM7XzjzLGg6GLOGEB8i5zVB9ovSiqRSCbtAwNVVdldvZuzh53dceO2i5xFKT4O7rPJ\nE2dgIMXHQgxKCQ8M3G4399xzD9nZ2VitVhYtWsSxY8divubRRx9l5syZOBwOhg0bxsKFC/nss88S\nfWh9Js+ax4uXvsiPZ/24vw9FiAEj25yNQTFwfsH5nW9sSIGJV8CYr8fcLMuSFbaiciTBGQMJDEQy\naZ9KVNlcSbWr+sz6BW05CrRUIlWNWXxsM9kiro0QSTCVSGoMhBhcEh4YLFmyhNdff51XXnmFzZs3\n09DQwJVXXonP54v6mg0bNnDnnXeydetW1q1bh8Fg4OKLL+b06c6LCgeqmXkz5U6JEG0sKFzA96d8\nH5spcjFxB9f8Ds77l5ibxDNjIKlEIhk5TI6wGYPd1bsBwguPg+z54HGCswZ87ug1BkYbTo8zrlaP\nssCZEINTQrsS1dfX88ILL7By5UouueQSAH77298yevRoPvjgAy699NKIr3vvvffCvv/tb39LWloa\nH330EQsXLkzkIQoh+sk/FP9DwveZac6ktqUWn98XtW5BUolEMmofGOyp3kOKPiWU6hq+caBlafUB\n7WuUwMBhcuBX/TR7m7EarTHf3+VxkaJPwaCT5odCDCYJnTHYsWMHHo+H+fPnhx4bOXIkJSUlbN26\nNe79NDY24vf7ycjISOThCSGGmCxLFipqaFYgEkklEsmofY3Bnuo9TMqahFEfoRlGMDCoOqh9jdGV\nCCIvnNZes7dZCo+FGIQSGhhUVFSg1+vJzs4Oezw3N5eKioq497N48WKmTp3K7NmyUrAQIrrQImcx\n6gzq3fVYDBZMelNfHZYQ/c5ustPia6HV14rH52H/qf2clX1W5I3bzxhEW+AsysJpkTR7miWNSIhB\nSFHjSBb8t3/7N37+85/H3Gb9+vWcOHGCG2+8EY/Hg6IooecuuugiJkyYwHPPPdfpAS1dupQ1a9aw\nZcsWxo4dG3GbFStWsGLFCgAOHjzIxIkTO2xTXV3NsGHDOn2/ZCfnKT6D+TyVlZVRU1PTo33ImEsc\nOU/xGcznScbcwCLnKT6D+TwlYswJTVyBQU1NTacnfNSoUfztb39j3rx5VFVVhX24Jk+ezNVXX81P\nf/rTmPu47777WLNmDevXr4/4S7ArZsyYwSeffNKjfSQDOU/xkfPUOTlH8ZHzFB85T52TcxQfOU/x\nkfMkIM7i4+zs7A7pQZFMnz4do9HI2rVrufZabbXfY8eOceDAAc4/P3aLwsWLF7NmzRo2bNjQ46BA\nCCGEEEII0TUJrTFIS0vj1ltv5YEHHuCDDz5g586d3HDDDZx99tlcfPHFoe0mTpzI008/Hfr+rrvu\nYuXKlbzyyitkZGRQUVFBRUUFTU3xLaQihBBCCCGE6JmE9xH77//+bwwGA9dccw0ul4t58+bx8ssv\no9efaSX4+eefh6UmPfvsswDMmzcvbF/Lli1j+fLl3TqO22+/vVuvSzZynuIj56lzco7iI+cpPnKe\nOifnKD5ynuIj50lAnDUGQgghhBBCiKEt4SsfCyGEEEIIIQYfCQyEEEIIIYQQQzMwePbZZyksLMRs\nNjN9+nQ2b97c34fUZzZt2sSiRYsYPnw4iqKwatWqsOdVVWX58uUUFBRgsVi48MIL2bdvX9g2tbW1\n3HDDDaSlpZGWlsYNN9xAXV30lWUHm0cffZSZM2ficDgYNmwYCxcu5LPPPgvbRs5T18iYkzEXi4y5\nxJMxJ2MuFhlzotvUIWbNmjWqwWBQV6xYoe7fv1+9++67VavVqh45cqS/D61P/OUvf1Efeugh9Y9/\n/KNqsVjUlStXhj3/2GOPqTabTX3ttdfUvXv3qt/97nfV/Px8taGhIbTNZZddpk6aNEn96KOP1K1b\nt6qTJk1Sr7zyyj7+SXrP/Pnz1RdffFHdu3evumfPHvXb3/62mpubq546dSq0jZyn+MmYkzHXGRlz\niSVjTsZcZ2TMie4acoHBueeeq/7gBz8Ie6yoqEh98MEH++mI+o/Vag37hen3+9W8vDz14YcfDj3W\n3Nys2mw29bnnnlNVVVX379+vAuqWLVtC22zevFkF1IMHD/bZsfelxsZGVafTqW+//baqqnKeukrG\n3Bky5uIjY65nZMydIWMuPjLmRLyGVCpRa2srO3bsYP78+WGPz58/n61bt/bTUQ0cpaWlVFRUhJ0f\ni8XCnDlzQudn27Zt2Gy2sAXpLrjgAqxW65A9h42Njfj9fjIyMgA5T10hYy42+SxFJmOu+2TMxSaf\npchkzIl4DanAoKamBp/PR25ubtjjubm5VFRU9NNRDRzBcxDr/FRUVDBs2DAURQk9rygKOTk5Q/Yc\nLl68mKlTpzJ79mxAzlNXyJiLTT5LkcmY6z4Zc7HJZykyGXMiXglf4GwgaPshBq3Apv1jyayz8xPp\nXA3Vc7h06VK2bNnCli1bwhbhAzlPXSFjLjb5LJ0hYy4xZMzFJp+lM2TMia4YUjMG2dnZ6PX6DpFs\nVVVVh6g4GeXl5QHEPD95eXlUVVWhtln3TlVVqqurh9w5vO+++3jllVdYt24dY8eODT0u5yl+MuZi\nk89SOBlzPSdjLjb5LIWTMSe6akgFBiaTienTp7N27dqwx9euXRuWI5esCgsLycvLCzs/LS0tbN68\nOXR+Zs+eTVNTE9u2bQtts23bNpxO55A6h4sXL2b16tWsW7eOiRMnhj0n5yl+MuZik8/SGTLmEkPG\nXGzyWTpDxpzolj4qcu4za9asUY1Go/qb3/xG3b9/v3rvvfeqVqtVLSsr6+9D6xONjY3qzp071Z07\nd6oWi0X96U9/qu7cuTPUxu6xxx5T7Xa7+vrrr6t79+5Vr7nmmojtyaZMmaJu27ZN3bp1qzplypQh\n1Z7szjvvVO12u/rhhx+qJ0+eDP1pbGwMbSPnKX4y5mTMdUbGXGLJmJMx1xkZc6K7hlxgoKqq+swz\nz6ijR49WTSaTOm3aNHXjxo39fUh9Zv369SrQ4c9NN92kqqrWomzZsmVqXl6empKSos6ZM0fdu3dv\n2D5OnTqlXnfddardblftdrt63XXXqbW1tf3w0/SOSOcHUJctWxbaRs5T18iYkzEXi4y5xJMxJ2Mu\nFhlzorsUVW2TPCaEEEIIIYRISkOqxkAIIYQQQgjRPRIYCCGEEEIIISQwEEIIIYQQQkhgIIQQQggh\nhEACAyGEEEIIIQQSGAghhBBCCCGQwEAIIYQQQgiBBAZCCCGEEEIIJDAQQgghhBBCIIGBSIDq6mry\n8/P52c9+Fnpsz549mM1mXnvttX48MiGGJhlzQvQtGXMiWSiqqqr9fRBi8HvvvfdYuHAhGzduZOrU\nqcyYMYNzzz2XlStX9vehCTEkyZgTom/JmBPJQAIDkTBLlizh7bffZu7cuWzevJldu3Zhs9n6+7CE\nGLJkzAnRt2TMiaFOAgORMG63m3POOYcvv/ySrVu3MmvWrP4+JCGGNBlzQvQtGXNiqJMaA5EwZWVl\nHD16FEVROHz4cH8fjhBDnow5IfqWjDkx1MmMgUgIj8fD7NmzKS4uZtasWSxfvpw9e/YwatSo/j40\nIYYkGXNC9C0ZcyIZSGAgEuLBBx9k9erV7Nmzh7S0NBYsWIDL5WL9+vXodDIxJUSiyZgTom/JmBPJ\nQD7Josc2btzIL37xC15++WXS09NRFIVVq1Zx4MABHn/88f4+PCGGHBlzQvQtGXMiWciMgRBCCCGE\nEEJmDIQQQgghhBASGAghhBBCCCGQwEAIIYQQQgiBBAZCCCGEEEIIJDAQQgghhBBCIIGBEEIIIYQQ\nAgkMhBBCCCGEEEhgIIQQQgghhEACAyGEEEIIIQTw/wFiKQaGMCanQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1094.5x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(wrap_as_xarray(integrated_untrained)\n",
    ".isel(time=[0, 2, 10], sample=[4, 10, 16])\n",
    ".plot(col='sample', hue='time', ylim=[-0.2, 0.5])\n",
    ")\n",
    "# untrained model is diverging! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 355,
     "status": "ok",
     "timestamp": 1564033400599,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "vB38PIDyfKGN",
    "outputId": "1005ae02-125f-4bb0-f486-f005e493a706"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 20,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# weights are initialized at the first model call\n",
    "len(model_nn.get_weights())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 483,
     "status": "ok",
     "timestamp": 1564033401176,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "qM674JcAfOYI",
    "outputId": "fa273c27-9bb2-4d05-f30c-c4ab9101b10d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1, 3, 32)"
      ]
     },
     "execution_count": 21,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_nn.get_weights()[0].shape # first convolutional filter, (x, y, input_channel, filter_channel) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 540,
     "status": "ok",
     "timestamp": 1564033401879,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "3MJ97azOfUj0",
    "outputId": "afc9b0f7-7fa4-47eb-a064-73c8a614a784"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1, 32, 32)"
      ]
     },
     "execution_count": 22,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_nn.get_weights()[2].shape # second convolutional filter, (x, y, filter_channel, filter_channel) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5OeI5-ooE6V_"
   },
   "source": [
    "# Generate training data from high-resolution baseline simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wHAQ6QB8E-84"
   },
   "outputs": [],
   "source": [
    "# This data-generation code is a bit involved, mostly because we use multi-step loss function.\n",
    "# To produce large training data in parallel, refer to the create_training_data.py script in source code.\n",
    "\n",
    "def reference_solution(initial_state_fine, fine_grid, coarse_grid, \n",
    "                       coarse_time_steps=128):\n",
    "\n",
    "  # use high-order traditional scheme as reference model\n",
    "  equation = advection_equations.VanLeerAdvection(cfl_safety_factor=0.5)\n",
    "  key_defs = equation.key_definitions\n",
    "\n",
    "  # reference model runs at high resolution\n",
    "  model = models.FiniteDifferenceModel(equation, fine_grid)\n",
    "  \n",
    "  # need 8x more time steps for 8x higher resolution to satisfy CFL\n",
    "  coarse_ratio = fine_grid.size_x // coarse_grid.size_x\n",
    "  steps = np.arange(0, coarse_time_steps*coarse_ratio+1, coarse_ratio)\n",
    "\n",
    "  # solve advection at high resolution\n",
    "  integrated_fine = integrate.integrate_steps(model, initial_state_fine, steps)\n",
    "\n",
    "  # regrid to coarse resolution\n",
    "  integrated_coarse = tensor_ops.regrid(\n",
    "      integrated_fine, key_defs, fine_grid, coarse_grid)\n",
    "  \n",
    "  return integrated_coarse\n",
    "\n",
    "\n",
    "def make_train_data(integrated_coarse, coarse_time_steps=128, example_time_steps=4):\n",
    "  # we need to re-format data so that single-step input maps to multi-step output\n",
    "\n",
    "  # remove the last several time steps, as training input\n",
    "  train_input = {k: v[:-example_time_steps] for k, v in integrated_coarse.items()}\n",
    "\n",
    "  # merge time and sample dimension as required by model\n",
    "  n_time, n_sample, n_x, n_y = train_input['concentration'].shape\n",
    "  for k in train_input:\n",
    "    train_input[k] = tf.reshape(train_input[k], [n_sample * n_time, n_x, n_y])\n",
    "\n",
    "  print('\\n train_input shape:')\n",
    "  for k, v in train_input.items():\n",
    "    print(k, v.shape)  # (merged_sample, x, y)\n",
    "\n",
    "  # pick the shifted time series, as training output\n",
    "\n",
    "  output_list = []\n",
    "  for shift in range(1, example_time_steps+1):\n",
    "    # output time series, starting from each single time step\n",
    "    output_slice = integrated_coarse['concentration'][shift:coarse_time_steps - example_time_steps + shift + 1] \n",
    "    # merge time and sample dimension as required by training\n",
    "    n_time, n_sample, n_x, n_y = output_slice.shape\n",
    "    output_slice = tf.reshape(output_slice, [n_sample * n_time, n_x, n_y])\n",
    "    output_list.append(output_slice)\n",
    "\n",
    "  train_output = tf.stack(output_list, axis=1)  # concat along shift_time dimension, after sample dimension\n",
    "\n",
    "  print('\\n train_output shape:',  train_output.shape)  # (merged_sample, shift_time, x, y)\n",
    "\n",
    "  # sanity check on shapes\n",
    "  assert train_output.shape[0] == train_input['concentration'].shape[0]  # merged_sample\n",
    "  assert train_output.shape[2] == train_input['concentration'].shape[1]  # x\n",
    "  assert train_output.shape[3] == train_input['concentration'].shape[2]  # y\n",
    "  assert train_output.shape[1] == example_time_steps\n",
    "\n",
    "  return train_input, train_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 179
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 12681,
     "status": "ok",
     "timestamp": 1564033415169,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "TwSKVyzbi4Ni",
    "outputId": "d31084a4-bf40-4a2f-c341-95d72949d252"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12 s, sys: 118 ms, total: 12.1 s\n",
      "Wall time: 12.2 s\n",
      "\n",
      " train_input shape:\n",
      "concentration (3750, 32, 1)\n",
      "x_velocity (3750, 32, 1)\n",
      "y_velocity (3750, 32, 1)\n",
      "\n",
      " train_output shape: (3750, 4, 32, 1)\n"
     ]
    }
   ],
   "source": [
    "# need to re-evaluate initial condition on high-resolution grid\n",
    "\n",
    "c_init_fine = make_multi_square(\n",
    "  x_fine,\n",
    "  height_list = height_list,\n",
    "  width_list = width_list\n",
    ")\n",
    "\n",
    "initial_state_fine = {\n",
    "    'concentration': c_init_fine.astype(np.float32),  # tensorflow code expects float32\n",
    "    'x_velocity': np.ones(c_init_fine.shape, np.float32) * 1.0,\n",
    "    'y_velocity': np.zeros(c_init_fine.shape, np.float32)\n",
    "}\n",
    "\n",
    "%time integrated_ref = reference_solution(initial_state_fine, fine_grid, coarse_grid)\n",
    "train_input, train_output = make_train_data(integrated_ref)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 307
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 588,
     "status": "ok",
     "timestamp": 1564033416022,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "IOHnCr4GjDd8",
    "outputId": "e772fe1b-5b15-4cdc-f8e3-fd3bd36c55ff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2018ed0400>"
      ]
     },
     "execution_count": 25,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
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CpCUk7uHsGOk3rPotjWvXMmD2bPpNm5b0nomRfhydDr51L1ywBLa/AGuvw2npC4Cn1QOA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\nQRCOIUT0BUEQjiFE9AVBEI4h/j9M42GV3c526AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make sure that single-step input corresponds to multi-step (advected) output\n",
    "\n",
    "i_sample = 48  # any number between 0 and train_output.shape[0]\n",
    "\n",
    "plt.plot(train_input['concentration'][i_sample].numpy(), label='init')\n",
    "for shift in range(train_output.shape[1])[:3]:\n",
    "  plt.plot(train_output[i_sample, shift].numpy(), label=f'shift={shift+1}')\n",
    "\n",
    "plt.title(f'no. {i_sample} sample')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mXMI-JNxFAaR"
   },
   "source": [
    "# Train neural net model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 1000
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 187378,
     "status": "ok",
     "timestamp": 1564033603504,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "Exzj2jB_FCDk",
    "outputId": "2f020fb4-ae7d-42e3-bc88-a81c7b840a79"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 3750 samples\n",
      "Epoch 1/80\n",
      "3750/3750 [==============================] - 7s 2ms/sample - loss: 0.0081 - root_mean_squared_error: 0.0253\n",
      "Epoch 2/80\n",
      "3750/3750 [==============================] - 2s 553us/sample - loss: 0.0017 - root_mean_squared_error: 0.0050\n",
      "Epoch 3/80\n",
      "3750/3750 [==============================] - 2s 525us/sample - loss: 0.0013 - root_mean_squared_error: 0.0042\n",
      "Epoch 4/80\n",
      "3750/3750 [==============================] - 2s 536us/sample - loss: 0.0011 - root_mean_squared_error: 0.0038\n",
      "Epoch 5/80\n",
      "3750/3750 [==============================] - 2s 577us/sample - loss: 0.0011 - root_mean_squared_error: 0.0037\n",
      "Epoch 6/80\n",
      "3750/3750 [==============================] - 2s 568us/sample - loss: 0.0010 - root_mean_squared_error: 0.0036\n",
      "Epoch 7/80\n",
      "3750/3750 [==============================] - 2s 591us/sample - loss: 0.0010 - root_mean_squared_error: 0.0035\n",
      "Epoch 8/80\n",
      "3750/3750 [==============================] - 2s 534us/sample - loss: 9.3966e-04 - root_mean_squared_error: 0.0034\n",
      "Epoch 9/80\n",
      "3750/3750 [==============================] - 2s 571us/sample - loss: 8.8812e-04 - root_mean_squared_error: 0.0033\n",
      "Epoch 10/80\n",
      "3750/3750 [==============================] - 2s 553us/sample - loss: 8.5974e-04 - root_mean_squared_error: 0.0033\n",
      "Epoch 11/80\n",
      "3750/3750 [==============================] - 2s 552us/sample - loss: 8.6032e-04 - root_mean_squared_error: 0.0033\n",
      "Epoch 12/80\n",
      "3750/3750 [==============================] - 2s 544us/sample - loss: 8.8654e-04 - root_mean_squared_error: 0.0034\n",
      "Epoch 13/80\n",
      "3750/3750 [==============================] - 2s 608us/sample - loss: 8.3509e-04 - root_mean_squared_error: 0.0033\n",
      "Epoch 14/80\n",
      "3750/3750 [==============================] - 2s 545us/sample - loss: 7.9731e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 15/80\n",
      "3750/3750 [==============================] - 2s 584us/sample - loss: 8.0802e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 16/80\n",
      "3750/3750 [==============================] - 2s 533us/sample - loss: 8.7171e-04 - root_mean_squared_error: 0.0033\n",
      "Epoch 17/80\n",
      "3750/3750 [==============================] - 2s 538us/sample - loss: 8.2093e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 18/80\n",
      "3750/3750 [==============================] - 2s 575us/sample - loss: 7.6915e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 19/80\n",
      "3750/3750 [==============================] - 2s 663us/sample - loss: 8.0100e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 20/80\n",
      "3750/3750 [==============================] - 2s 637us/sample - loss: 7.7220e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 21/80\n",
      "3750/3750 [==============================] - 2s 548us/sample - loss: 7.9108e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 22/80\n",
      "3750/3750 [==============================] - 2s 571us/sample - loss: 7.5859e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 23/80\n",
      "3750/3750 [==============================] - 2s 564us/sample - loss: 7.8670e-04 - root_mean_squared_error: 0.0032\n",
      "Epoch 24/80\n",
      "3750/3750 [==============================] - 2s 573us/sample - loss: 7.2347e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 25/80\n",
      "3750/3750 [==============================] - 2s 573us/sample - loss: 7.7214e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 26/80\n",
      "3750/3750 [==============================] - 2s 548us/sample - loss: 7.5216e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 27/80\n",
      "3750/3750 [==============================] - 2s 542us/sample - loss: 7.7241e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 28/80\n",
      "3750/3750 [==============================] - 2s 555us/sample - loss: 7.6037e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 29/80\n",
      "3750/3750 [==============================] - 2s 529us/sample - loss: 7.2885e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 30/80\n",
      "3750/3750 [==============================] - 2s 569us/sample - loss: 7.5086e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 31/80\n",
      "3750/3750 [==============================] - 2s 651us/sample - loss: 7.3128e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 32/80\n",
      "3750/3750 [==============================] - 2s 609us/sample - loss: 7.2566e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 33/80\n",
      "3750/3750 [==============================] - 2s 565us/sample - loss: 6.9604e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 34/80\n",
      "3750/3750 [==============================] - 2s 561us/sample - loss: 7.9358e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 35/80\n",
      "3750/3750 [==============================] - 2s 563us/sample - loss: 7.0298e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 36/80\n",
      "3750/3750 [==============================] - 2s 557us/sample - loss: 7.5806e-04 - root_mean_squared_error: 0.0031\n",
      "Epoch 37/80\n",
      "3750/3750 [==============================] - 2s 575us/sample - loss: 7.0112e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 38/80\n",
      "3750/3750 [==============================] - 2s 569us/sample - loss: 6.8068e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 39/80\n",
      "3750/3750 [==============================] - 2s 544us/sample - loss: 6.8285e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 40/80\n",
      "3750/3750 [==============================] - 2s 535us/sample - loss: 6.6481e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 41/80\n",
      "3750/3750 [==============================] - 2s 545us/sample - loss: 6.7487e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 42/80\n",
      "3750/3750 [==============================] - 2s 559us/sample - loss: 6.9282e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 43/80\n",
      "3750/3750 [==============================] - 2s 598us/sample - loss: 6.7989e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 44/80\n",
      "3750/3750 [==============================] - 2s 559us/sample - loss: 6.8837e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 45/80\n",
      "3750/3750 [==============================] - 2s 561us/sample - loss: 6.8555e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 46/80\n",
      "3750/3750 [==============================] - 2s 608us/sample - loss: 6.8288e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 47/80\n",
      "3750/3750 [==============================] - 2s 548us/sample - loss: 6.8992e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 48/80\n",
      "3750/3750 [==============================] - 2s 560us/sample - loss: 6.6419e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 49/80\n",
      "3750/3750 [==============================] - 2s 566us/sample - loss: 6.5738e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 50/80\n",
      "3750/3750 [==============================] - 2s 602us/sample - loss: 7.0420e-04 - root_mean_squared_error: 0.0030\n",
      "Epoch 51/80\n",
      "3750/3750 [==============================] - 2s 528us/sample - loss: 6.2609e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 52/80\n",
      "3750/3750 [==============================] - 2s 526us/sample - loss: 6.6002e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 53/80\n",
      "3750/3750 [==============================] - 2s 596us/sample - loss: 6.5252e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 54/80\n",
      "3750/3750 [==============================] - 2s 564us/sample - loss: 6.5228e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 55/80\n",
      "3750/3750 [==============================] - 3s 672us/sample - loss: 6.5959e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 56/80\n",
      "3750/3750 [==============================] - 2s 618us/sample - loss: 6.6641e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 57/80\n",
      "3750/3750 [==============================] - 2s 604us/sample - loss: 6.5434e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 58/80\n",
      "3750/3750 [==============================] - 3s 701us/sample - loss: 6.4204e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 59/80\n",
      "3750/3750 [==============================] - 3s 784us/sample - loss: 6.5064e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 60/80\n",
      "3750/3750 [==============================] - 2s 622us/sample - loss: 6.2518e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 61/80\n",
      "3750/3750 [==============================] - 2s 534us/sample - loss: 6.2716e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 62/80\n",
      "3750/3750 [==============================] - 2s 546us/sample - loss: 6.4124e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 63/80\n",
      "3750/3750 [==============================] - 2s 542us/sample - loss: 6.1816e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 64/80\n",
      "3750/3750 [==============================] - 2s 580us/sample - loss: 6.1458e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 65/80\n",
      "3750/3750 [==============================] - 2s 596us/sample - loss: 6.5261e-04 - root_mean_squared_error: 0.0029\n",
      "Epoch 66/80\n",
      "3750/3750 [==============================] - 2s 557us/sample - loss: 6.2476e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 67/80\n",
      "3750/3750 [==============================] - 2s 555us/sample - loss: 6.2833e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 68/80\n",
      "3750/3750 [==============================] - 2s 558us/sample - loss: 6.3743e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 69/80\n",
      "3750/3750 [==============================] - 2s 597us/sample - loss: 6.4814e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 70/80\n",
      "3750/3750 [==============================] - 2s 543us/sample - loss: 6.1840e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 71/80\n",
      "3750/3750 [==============================] - 2s 560us/sample - loss: 6.0522e-04 - root_mean_squared_error: 0.0027\n",
      "Epoch 72/80\n",
      "3750/3750 [==============================] - 2s 566us/sample - loss: 5.9715e-04 - root_mean_squared_error: 0.0027\n",
      "Epoch 73/80\n",
      "3750/3750 [==============================] - 2s 547us/sample - loss: 6.4651e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 74/80\n",
      "3750/3750 [==============================] - 2s 559us/sample - loss: 6.2796e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 75/80\n",
      "3750/3750 [==============================] - 2s 571us/sample - loss: 6.2158e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 76/80\n",
      "3750/3750 [==============================] - 2s 568us/sample - loss: 5.9102e-04 - root_mean_squared_error: 0.0027\n",
      "Epoch 77/80\n",
      "3750/3750 [==============================] - 2s 561us/sample - loss: 6.4003e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 78/80\n",
      "3750/3750 [==============================] - 2s 540us/sample - loss: 6.1087e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 79/80\n",
      "3750/3750 [==============================] - 2s 541us/sample - loss: 6.3195e-04 - root_mean_squared_error: 0.0028\n",
      "Epoch 80/80\n",
      "3750/3750 [==============================] - 2s 522us/sample - loss: 6.1190e-04 - root_mean_squared_error: 0.0027\n",
      "CPU times: user 8min 51s, sys: 1min 13s, total: 10min 5s\n",
      "Wall time: 3min 6s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "# same as training standard Keras model\n",
    "model_nn.compile(\n",
    "    optimizer=tf.keras.optimizers.Adam(0.001 * 1), loss='mae',\n",
    "    metrics=[tf.keras.metrics.RootMeanSquaredError()]\n",
    "    )\n",
    "\n",
    "tf.random.set_random_seed(42)\n",
    "np.random.seed(42)\n",
    "history = model_nn.fit(\n",
    "    train_input, train_output, epochs=80, batch_size=32, \n",
    "    verbose=1, shuffle=True\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 291
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 594,
     "status": "ok",
     "timestamp": 1564033604243,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "MKN202HjmUtR",
    "outputId": "7a3d0d4f-2ff5-4df2-8676-e5e95f4c38d9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f201a8ff710>"
      ]
     },
     "execution_count": 27,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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POA2AZs2aZVCmMTyafxggMv/11bK+tlgiPKx82IpvjHjfu30doIauPumF6btAo9GI/8/J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\nxhhjHcbhwRhjrMP+fxdn+rJndW2tAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_history = pd.DataFrame(history.history)\n",
    "df_history.plot(marker='.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 291
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 545,
     "status": "ok",
     "timestamp": 1564033605012,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "258zBdFlowSm",
    "outputId": "0724c4d5-30ce-4b06-fee9-357ed83fe104"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2015414b38>"
      ]
     },
     "execution_count": 28,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NbXoIOMDI7C85k1VUjTa9qbVo3iDtVls1wMdNAsDUv7X9ubhbrv6EDFUcM/e+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\nBSUYQgghTkEJhhBCiFNQgiGEEOIU/x9yaY8UwWE1OgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_history['loss'][3:].plot(marker='.')\n",
    "# might not converged yet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EkTO22vnFDib"
   },
   "source": [
    "# Integrate trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 53
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2617,
     "status": "ok",
     "timestamp": 1564033607744,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "P9arX3nQFHGD",
    "outputId": "3bc3d183-3d40-485a-de9d-86764dfd394b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.08 s, sys: 78.4 ms, total: 2.15 s\n",
      "Wall time: 2.08 s\n"
     ]
    }
   ],
   "source": [
    "%time integrated_nn = integrate.integrate_steps(model_nn, initial_state, time_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 35
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 499,
     "status": "ok",
     "timestamp": 1564033608469,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "JotBMxhnnskT",
    "outputId": "377d59ae-939d-497a-ef44-181dcbd6def7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Frozen(OrderedDict([('time', 129), ('sample', 30), ('x', 32)]))"
      ]
     },
     "execution_count": 30,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dr_nn = wrap_as_xarray(integrated_nn)\n",
    "dr_nn.sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 236
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1032,
     "status": "ok",
     "timestamp": 1564033609580,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "Ezk-6D3SpMCj",
    "outputId": "1c4419ae-32c2-40eb-e48b-de3ca24687e4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.plot.facetgrid.FacetGrid at 0x7f2015363780>"
      ]
     },
     "execution_count": 31,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CaqoyEBJAiN5HAgghRI+yv6UWnGVMP3E6Y4rG6Nv4GzMg6IdL/wSmw2c9XBYX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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1107.12x300 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dr_nn.isel(time=[0, 10, 128], sample=[4, 10, 16]).plot(col='sample', hue='time')\n",
    "# much better than traditional finite difference scheme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pM0Ow3vLFHkO"
   },
   "source": [
    "# Evaluate accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jehH8qpcfQqX"
   },
   "source": [
    "Here just test on training data. You can also make new test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Mwl2xSs1FIuT"
   },
   "outputs": [],
   "source": [
    "dr_ref = wrap_as_xarray(integrated_ref)  # reference \"truth\"\n",
    "\n",
    "dr_all = xarray.concat([dr_nn, dr_2nd, dr_1st, dr_ref], dim='model')\n",
    "dr_all.coords['model'] = ['nn', '2nd', '1st', 'ref']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 668
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2786,
     "status": "ok",
     "timestamp": 1564033612958,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "dUxqSq2zr_O5",
    "outputId": "6cc04f3b-cc0f-487f-be39-ccc352e982c0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.plot.facetgrid.FacetGrid at 0x7f20147afb00>"
      ]
     },
     "execution_count": 33,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JuoiIiIiIiEiAUJIuIiIiIiIiEiCUpIuIiIiIiIgECCXpIiIiIiIiIgFCSbqIiIiIiIhI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\nufnmm7nlllu49NJLiY+PZ82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haAMAI50uzqrvx36bDUe8f2dwP1UOmwV3VBxGUyzXt0Tx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\nD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hjRh/z85z/nwIED3HrrrcM+/6tf/Ypf/epXAHR0OHDjqOUACETLxv+zzxDFH0QHjEza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\nhCTpQgghhBBCCCFEgvj/dtjdMzod/6EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1407x900 with 12 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(dr_all.isel(time=[0, 16, 64, 128], sample=[4, 10, 16])\n",
    ".plot(hue='model', col='time', row='sample', alpha=0.6, linewidth=2)\n",
    ")\n",
    "# neural net model (blue line) almost overlaps with reference truth (red line); so lines are hard to see clearly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {
     "height": 307
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 638,
     "status": "ok",
     "timestamp": 1564033613679,
     "user": {
      "displayName": "Jiawei Zhuang",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mBNjea_sdhO3dTwm9O50BCtKFCEyd8kuD9gDROU=s64",
      "userId": "08419589760845158989"
     },
     "user_tz": 420
    },
    "id": "1lByshmolDdJ",
    "outputId": "a72a993a-0527-40bd-df43-901dcef6679f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0t4zUFdCsMzywWDPPQG4ViVvMoMQwcuRIcnJymD9/PhkZGYSGhhIXF4e/vz+A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\nYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "(\n",
    "  (dr_all.sel(model=['nn', '1st', '2nd']) - dr_all.sel(model='ref'))\n",
    "  .pipe(abs).mean(dim=['x', 'sample'])  # mean absolute error\n",
    "  .isel(time=slice(0, -1, 2))  # the original error series oscillates between odd & even steps, because CFL=0.5\n",
    "  .plot(hue='model')\n",
    ")\n",
    "plt.title('mean absolute error')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YVTWf1ETlShj"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "last_runtime": {
    "build_target": "//research/biology/collaborations/superres:notebook",
    "kind": "shared"
   },
   "name": "tutorial-advection-1d.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
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